Theories of Everything with Curt Jaimungal - A (Gentle) Introduction to Quantum Computing | Maria Violaris

Episode Date: December 17, 2024

Head over to https://www.masterclass.com/theories for the current offer. MasterClass always has great offers during the holidays, sometimes up to as much as 50% off. In today's episode of Theories of Everything, Curt Jaimungal speaks to Maria Volaris for a gentle introduction to quantum computing, diving into quantum no-go theorems, Schrödinger's cat, the nature of quantum entanglement, and how these concepts lay the foundation for the future of computational science. As a listener of TOE you can get a special 20% off discount to The Economist and all it has to offer! Visit https://www.economist.com/toe LINKS MENTIONED: •⁠ ⁠Maria Violaris’s OSV profile: https://www.osv.llc/fellows-grantee/maria-violaris •⁠ ⁠Maria’s YouTube channel: https://www.youtube.com/@maria_violaris/videos •⁠ ⁠Maria’s series on Qiskit: https://www.youtube.com/watch?v=Pz829XZIxXg •⁠ ⁠Chiara Marletto on TOE: https://www.youtube.com/watch?v=40CB12cj_aM •⁠ ⁠Curt Jaimungal’s Substack: https://curtjaimungal.substack.com/ Timestamps: 00:00 - Introduction 00:59 - Maria’s Background 04:20 - Quantum No-Go Theorems 09:55 - Schrödinger's Cat 13:41 - Theory Independence & Loopholes 17:21 - Uncertainty Principle (Entanglement) 23:11 - Qubits (Quantum Bit) 31:58 - Bell’s Theorem (Quantum Entanglement) 45:12 - Locality & Realism 49:04 - Bell’s Theorem Continued… 01:00:06 - GHZ States New Substack! Follow my personal writings and EARLY ACCESS episodes here: https://curtjaimungal.substack.com TOE'S TOP LINKS: - Enjoy TOE on Spotify! https://tinyurl.com/SpotifyTOE - Become a YouTube Member Here: https://www.youtube.com/channel/UCdWIQh9DGG6uhJk8eyIFl1w/join - Support TOE on Patreon: https://patreon.com/curtjaimungal (early access to ad-free audio episodes!) - Twitter: https://twitter.com/TOEwithCurt - Discord Invite: https://discord.com/invite/kBcnfNVwqs - Subreddit r/TheoriesOfEverything: https://reddit.com/r/theoriesofeverything #quantumphysics #science #physics #quantumcomputing #theoreticalphysics Learn more about your ad choices. Visit megaphone.fm/adchoices

As a Fizz member, you can look forward to free data, big savings on plans, and having your unused data roll over to the following month, every month. At Fizz, you always get more for your money. Terms and conditions for our different programs and policies apply. Details at fizz.ca. Bumble knows it's hard to start conversations. Hey. No, too basic. Hi there. Still no. What about hello handsome? Who knew you could give yourself the ick? That's why Bumble is changing how you start conversations. You can now make the first move or not. With opening moves, you simply choose a question to be automatically sent to your matches.

Then sit back and let your matches start the chat. Download Bumble and try it for yourself. This podcast serves both as an introduction to quantum mechanics and quantum computing. sit back and let your matches start the chat. Download Bumble and try it for yourself. physics and philosophy in front of you in podcast form, bridging these disparate subjects and making abstract concepts digestible while not skimping on nor being afraid of the technicalities. Today I thought it would be fantastic to give an overview of some of the no-go theorems in basic quantum theory. They're explained both rigorously and the intuition behind them is provided. I'm excited to say that Maria Villaloros covers what realism actually means, what is non-locality, what is the Koch and Specker theorem, Bell's inequalities, the Leggett inequalities, contextuality, loopholes, quantum gates, qubits, entanglement, separability, GHZ states, and many more, all

succinctly in 1.5 hours. Start off by telling us about your journey into physics, where you started, what changed along the way, where are you now, where are you headed? Yeah, sure. So my journey into physics started near the end of high school is when I started getting interested in physics, in particular quantum physics. I was intrigued by popular science articles about things being in two places at once and that kind of thing, and also aspects of thermodynamics and ideas about entropy and information. So that's what persuaded me to then do a physics degree afterwards.

So I studied physics Oxford, and then I became interested in a particular approach to unifying aspects of physics called Constructor Theory. So I know you've interviewed Chiara Maleta on your podcast before. I became interested in her work when I was in undergrad. It turned out that her and David Deutsch were in Oxford. And so I started working with them during my master's project. And then I was enjoying the work that I was doing on quantum and thermodynamics as part of that theory. So that led me to continue to do a PhD. So I did a PhD in the foundations of quantum information in Vlad K. Vedrov's group in Oxford. And I just finished that a few months ago.

In August was my final VIVA assessment. And alongside that, I was also making videos working with IBM Quantum, making videos about resolving quantum paradoxes using quantum computing. And I've also kind of been involved in the quantum computing area and in generally doing outreach and engagement quite a lot since over the last few years. And now I'm working at Oxford Quantum Circuits, which is a startup, well, scale up, it's been around a few years now and I'm partly working on quantum error correction research and partly working on doing science communication and content in a kind of hybrid role.

So yeah, that's been my journey kind of across industry, academia and engagement with quantum. And I also have continued with the content creation myself as well, posting videos on my channel and trying to share more quantum content. Your channel is Maria Villalauris, and the link will be on screen and in the description. If you are from the Toa audience and you're going over to hers, which I do recommend you do and you subscribe, then comment and say, Kurt sent you. Yeah, look forward to the comments. Okay, great.

And you're also on KISSKit, correct? Yeah. So that was the internship that I was doing part-time alongside my PhD was with KISSKit and I made a series of videos on a playlist called Quantum Paradoxes. So if you just search Quantum Paradoxes into Google, then that playlist comes up with 15 videos. Yeah, they kind of, they expect some introductory background to quantum computing that you can get from other resources and then they explain various thought experiments using quantum computing.

Many people who watch the Theories of Everything podcast, this program, are academic researchers in physics, but many are also just academic researchers in various disciplines like computer science, philosophy, math. So while the former physics may be aware of the quantum no-go theorems and related concepts that you're about to cover, the latter may not be. So I'm extremely, extremely excited about this. Why don't you just take it away? Yeah, great. So yeah, today I'm going to talk about these quantum no-go theorems. So one of the most famous of these is Bell's theorem. So it's very

commonly discussed in popular science and it's also the topic that led to the Nobel Prize a few years ago. So it's kind of sparked lots of recent discussion as well. And it's also been exactly 60 years since Bell's theorem. So there's been a few celebrations this year on anniversary of Bell and also all of the progress that's been made since then, and also the questions that are still unanswered. So it's an interesting time to be discussing it. And what I'm going to do is try and give an overview of Bell's theorem and the other no-go theorems that have, they're all kind of some variation

of Bell in a sense, since Bell was proposed. And I'll try and give an idea for how they tell us different things about the nature of reality and also where our modern understanding of this is. Matthew 4.14 Wonderful. Sam 4.14 Here I've just put a kind of a summary of the different theorems that will come up. So first we have Bell's theorem, which was proposed in 1964, 60 years ago. I'll come on to exactly what it is. And it was kind of developed into a particular kind of inequality called the CHSH inequality and then further developed into a thought experiment involving GHZ states,

which we'll talk about. And the kind of point of this theorem and the variations, the ways of testing it are to rule out a certain class of theories for describing quantum mechanics called local hidden variable models. So we'll talk more about what they are and Bell's theorem provides a statistical way of ruling these out, whereas these GHZ states provide a deterministic way of ruling out these theories. And then we'll move on to another theorem called the Koch and Specker theorem. So this is kind of similar to Bell, but we'll see that it's a bit different in that it rules out a different class of theories. Instead of ruling out local hidden variable

models, it's going to rule out another type of theory called non-contextual hidden variable models. And this will lead us to understanding a certain property in quantum mechanics that has triggered lots of research called contextuality. So we'll come on to what that is. Then I'll talk about another type of theorem based on the Leggett-Garg inequalities. So the idea of these is to test a feature called macro realism, which is to do with the properties of macroscopic large systems. And so we'll talk about what that theorem tells us and also how it's being used to come up with tests for systems behaving

in a quantum way. So that's what we mean by quantum witness. And finally, we'll talk about the PBR theorem. So this is the most recent one from this set proposed in 2012. The point of this is to consider whether the quantum wave function is part of a physical property of reality, or if we can somehow think of it as just telling us information about what is actually a physical property. So these different outlooks are called Psi-Epistemic is the idea of just giving information about what's actually out there, just revealing some distribution about what's out there, whereas psionic is the idea of actually physically being part of the systems that are out there.

So we'll come on to what this theorem is telegasted also, how it compares back to Bell's theorem and we'll see that it's actually got very similar connections with Bell. Great. And just for people who are tuning in, Maria will be defining the different terms. I know you just heard quite a few different theorems, which may be unfamiliar to you. And then there are ingredients to those theorems like contextuality or non-contextuality or realism, macro-realism, epistemic, ontic, locality, non-locality, and so on. So as this conversation progresses,

there will be definitions. Yeah, great. So let's start with some background then to kind of set the scene, trying to make the accessibility as broad as possible. So I wanted to kind of go back to the beginning of what these questions are that have been troubling people about quantum mechanics and these ideas will kind of come up again and again in terms of interpreting what these no-go theorems are telling us and also motivating why we want to use no-go theorems to tell us things about quantum mechanics. So the kind of most famous implication of quantum theory is Schrodinger's cats become a big meme. I also quantum theory is Schrodinger's cat has become a big meme.

And I also carry around a Schrodinger's cat with me to demonstrate it. So this is the idea that we have this consequence of quantum theory that leads to the seeming possibility of a cat being dead and alive at the same time in a superposition of being dead and alive if we describe it with quantum mechanics. And this kind of leads to a debate which is still going on today, which is either that quantum theory applies on all scales, including to macroscopic objects like cats, with an implication of that being that these superpositions of being dead and alive must be possible. Or perhaps there's some scale where quantum theory doesn't apply anymore and there's some kind of irreversible collapse

that comes in to prevent macroscopic systems from being in soup positions. So there's this question about soup position that comes up again and again, when interpreting what quantum theory is telling us about reality. And it's closely related to what measurement of a system is because of this issue of perhaps a measurement is causing an irreversible collapse at some scale. Then we have another kind of core idea that comes up again and again and again is to do with the incompleteness of quantum theory. There's a famous paradox, the EPL paradox from Einstein, Podolsky and Rosen. And they were thinking about quantum entanglement, which is a property that you

can have of quantum systems that you prepare a certain way. And then they become correlated more than you can get from classical physics, which we'll come on to in more detail because it's very relevant for Bell's theorem that we'll talk about. And they found this entanglement property of quantum theory problematic because it seemed to allow for aspects of quantum theory that weren't consistent with other principles of physics, such as the no faster than light influences constraints from special relativity. And so this led them to propose that perhaps quantum theory is incomplete as a theory. There's something additional to add to it to make it make sense. And one of the proposals for making it make sense was to describe it by a local hidden variable model.

So we'll come on to what that is and what happens when we try and describe it that way. And so overall we have this kind of question of what can we conclude about the nature of reality given the outcomes of experiments. And that's what the Nogo theorems about is trying to conclude answers to these questions about what is quantum mechanics telling us about reality. And here I just kind of listed some of the key concepts that will come up. So we've mentioned detanglement and measurement, and we'll talk more about what Heisenberg's Assertive Principle is, what we mean by realism and elements of reality.

I also thought it would be useful to introduce what qubits are, so I'm going to do that in a moment because I'll be using them as a tool to explain what the Nogo theorems tell us. Okay, so there are two terms here that may be unfamiliar to people. Theory independence and loopholes. Why don't you outline what those mean? Struggling with gift ideas? This holiday season, I found a solution that's both thoughtful and practical.

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So these are kind of relating to the general spirit of what no-go theorems like Bell's tell us. So one interesting aspect that some of the no-go theorems have, not all of them, but it's something that people kind of trying to get them to have is theory independence. to get them to have is theory independence. So the idea of this is to try and develop your theorem such that it will tell you something about reality regardless of whether or not it's quantum mechanics that it's being applied to. So what people really like about Bell's theorem, which we'll talk about is that when you take the measurements, it tells you something about whichever theory turns out to be describing the world, even if it turns out different from what quantum theory is actually as we've

developed it. So that's a kind of goal of these Nogo theorems is often to have this theory independence property, which is kind of quite robust. Interesting. And the other kind of keyword is to do with loopholes. So in the Nobel Prize awarded for Bell's theorem, one key aspect was the performance of experiments that demonstrate it without certain loopholes. experiments that demonstrate it without certain loopholes. Maybe reality is modified in a way that gets around the theorem somehow and these loopholes need to be closed in order

to show that the theorem kind of really robustly applies. So that term might come up as well. Yeah, I've already introduced Schrodinger's cat and Tangoma. Yeah, I've already introduced Sridhargis and Entanglement. Yeah, I wanted to kind of introduce the uncertainty principle as well, because this is what kind of tells us what's actually strange about Entanglement. When I introduce Entanglement, I like to explain it using like a pair of socks. You just take your socks out and look at them, then they're going to be correlated. So let's say they're both pink, then if you know that one is pink, then you know that the other is pink.

And this is an example of classical correlation. But in quantum theory, particles can instead be quantum correlated in such a way that they're correlated in a stronger way than the pair of socks is correlated. So to kind of think about this, I like to think about say two different properties of the socks. One property can be the colour, it could be pink or blue, and another property could be the size, so it could be small or large. And then the uncertainty principle in quantum mechanics essentially says that quantum systems can have properties such that

you can't measure the values of both of those properties simultaneously. So if you measure the value of one of them, you become uncertain about the value of the other. So that's like saying if you can measure the color of a sock, then you become uncertain about the size. The all-new FanDuel Sportsbook in Casino is bringing you more action than ever. Want more ways to follow your faves? Check out our new player prop tracking with real-time notifications.

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If you or someone you know has concerns about gambling, visit connectsontario.ca. But what we find in quantum mechanics with entangled particles is that you could measure one property, or you could measure the other property on the two systems and you'll find that they're correlated with whichever property you measure as long as you measure the same one on both systems. And that's the kind of strange thing about these extra correlations that you get with entanglement compared to classical correlations is that even though when you measure one property it makes the other one completely random, somehow it seems like these quantum systems know to always give the same one when you measure it in distant places. So that's the kind of strangeness on top of- So just a moment.

Yeah. Earlier you said when you take a look at these socks, they're correlated, but a classical correlation would be more like you're given a box, you're told it has socks in it. You pull out one of the socks, it's pink. You trust the manufacturer that the manufacturer is not tricking you. So you infer that the other sock is pink. So is it that we're looking at it and then that correlates it? Or is it that we're just supposed to know that socks come in pairs and we're dealing with that pair? A classical correlation.

Yeah, yeah, I think the way you explained it in terms of looking at it. And then since you know that the socks come in pairs of the same color, then when you look at it, you can deduce that the other one must have the same color. Okay. That's the classical case, yeah. And then the second question is, when you were saying that if you make one measurement, one type of measurement, namely sock color,

that the second one is then correlated, namely sock length. Is that what you're referring to? So if you look at it and you say pink, not only can you infer that the second one is pink, but you somehow infer something about the size of both of them? I'm saying something a bit different in that you can either observe the colour or observe the size. So you get to choose which one of those you're going to observe. If you observe the colour, then with quantum entanglement, you can immediately infer that the other will be the same colour.

If you instead infer the size, you can immediately infer that the other one will be the same size, if you measure the size, sorry. In the classical case with real socks, that's fine, like that's what we expect. The strangeness comes from the fact that we have this uncertainty principle. So if we try and imagine that there was a principle that means that a sock cannot have definite size and definite color simultaneously. That's when it's strange that it's always correlated in whichever property you choose to measure, whether you choose to measure size or whether you choose to measure color. Even though the other sock didn't have a definite state in both of those

properties, somehow it's always measured to agree with your sock. The strangeness is that somehow the measurements on the two sides conspired to agree with each other even though it can't have had a definite property of both colour and size or both of these properties. Okay got it because people are watching and then thinking okay there's nothing spooky here, we do this all the time with socks like we mentioned, so why is it spooky when it comes to particles that they're correlated? And firstly here is this assuming a local hidden variable if we were to translate it to quantum mechanics or not yet?

local hidden variable if we were to translate it to quantum mechanics or not yet? So I'd say that this is the kind of the idea of why it's strange. And then a local hidden variable model is something that you can introduce to try and explain away the strangeness to kind of make sense of it. And then we'll see that doesn't work as a way of trying to save the correlations from being so strange. This will come up again later. And the other thing I wanted to kind of introduce is the idea of a qubit, because I'll be using this to kind of explain some of the ideas and also how they're experimentally implemented and tested. The idea of a qubit is that it stands for quantum bit, that's where the word qubit comes

from. People tend to be used to the idea of classical bits, which are expressed in terms of ones and zeros. Usually that's how all of our classical computers are encoded in terms of ones and zeros. And we can kind of think of it in terms of heads and tails on a coin. Instead, you can think of a qubit as being like a sphere. So I have my own model one where the top is the zero state, the bottom is the one state, and every other point on the surface of the sphere is a superposition of zero and one. Each of the points of the sphere is a unique, different quantum state. And when you measure the qubit, it gets projected into either the zero or the one state with some probability. And that probability is determined by how close it is, the state is to zero or to one.

So if it's close to zero, it's got a high probability of getting projected to zero, low probability of getting projected to zero, low probability of getting projected to one. And this is what quantum computers are based on. They're built out of these qubits. And I like to think of the superstition state of zero and one as like the coin spinning being in this superstition of the heads and tails. And I'm just going to kind of introduce the basics of how we manipulate qubits. So when you think of bits, the way that you can manipulate them is you can turn a zero to a one, a one to a zero. So that's like doing a flip of the coin.

But when you have qubits and you have a sphere, there's a lot more you could do. You can actually, for a single qubit, you can do rotations around the sphere. And these are called the quantum gates. So one rotation you can do is called an X flip. So that's, it's like the flipping a coin. You go from zero, takes you from zero to one, or from one to zero. Another rotation you can do is called the Hadamard gate. So this takes you from, it takes zero to a superposition, and it takes a superposition back to zero. So that's like sending the coin spinning or stopping a spinning coin from spinning back into one state. stopping a spinning coin from spinning back into one state. And the cool gate that we need to create entanglement is called a control not gate. So the idea here is that we have a qubit that we've set spinning that we've put in superposition.

We have another qubit that's just in our zero state. And then what this control-not gate does is if the first qubit was in the zero state, it leaves the second qubit being zero. If the first qubit was in the one state, it flips the second qubit, so it's flipped to one. And so it essentially kind of shifts its state onto the other qubits so that they both become correlated. And then we represent the resulting two qubit state like this. And this is an entangled state where we've entangled the two qubits and you can represent it as 00 plus 11. So this notation is called Dirac notation. It's a way of representing quantum states. And the nice thing about it is that even though there's a powerful mathematical background

to it, we can intuitively understand what it's telling us, which is by essentially these kind of numbers are labelling what state the qubit is in, and the plus means that we've put them into superposition. So this notation will be useful for giving some idea of what's going on in aspects of these quantum theorems. Fantastic. I want this to be extremely simple and introductory for people, but at the same time I want to be technically precise. So when you have this circle, this sphere, and you have a line, if you don't mind holding that up again, people may look at that and if they're not physicists, they may think, okay, I've heard that electrons are what some people use for quantum computers or photons.

Am I supposed to think of a photon as this sphere carrying with it a direction or is that something abstract? Is that something else that goes into photons pocket that carries along with it? Explain how are people supposed to understand this sphere? Yeah, so the sphere is like an abstract representation for that directly maps onto lots of different physical ways that you can implement a qubit, in the same way that there's lots of different ways you could physically implement a bit. You just need any physical system that can be in two states and then a way of controlling it between those states.

A photod, like you mentioned, is actually one of the implementations I like the most in terms of being able to visualize what is actually happening. So the example that I like to use in terms of a photon is to think about a photon going through a beam splitter. So the idea is that a beam splitter is like a half silvered mirror and what you can do is take a single photon to the beam splitter and then it splits into a supposition of being reflected and then going straight through. And the way that you can understand this abstractly in terms of the sphere is that let's say the horizontal state that it began in is the zero state.

And then it hits the BSP filter, it gets put into this superposition of carrying on horizontal, so carrying on the zero, but also being reflected and let's call that the one state, the vertical pathway. And so it's gone from zero to a sub-position of zero and one. And so what that corresponds to on the sphere is that it's gone from this fixed state at the top and it's the beam splitter, this half-silver mirror has rotated it to this supposition state of zero one. So the beam splitter is a way of implementing this Hadamard gate. And it's a way of performing this kind of abstract rotation from zero to zero and to the supposition of zero one physically. Great.

Okay. Now for the photon, if we get that ball and we have the up and the down, are people supposed to think of this as the photons spin up and spin down, or are people supposed to think about this as a polarization, or is it something else? Yeah, so there's lots of different ways you can encode the information even for a photon. So, one of them is as pathways. So in the example I mentioned, the information even for a photon. So one of them is as pathways. So in the example I mentioned, the information would be encoded in the pathway of zero is horizontal, one is vertical, and you can create superstitions of that. Another way you can encode it is in terms of polarisation.

So that's a certain property of photons, they can be polarised horizontally or vertically, and you can use optical devices to get the photon's polarisation to shift, and that's actually the most kind of common one in terms of where we're actually trying to control things with photons is to manipulate polarisation. Another cool one is actually just the existence of the photon or not. So you can have zero being the vacuum state of no photon existing and one being the state of a photon existing.

Um, interesting. And if, if we were using an electron instead, then we could encode it in spin. if we were using an electron instead, then we could encode it in spin. And that's a common way when we're using particles such as electrons, then the property of spin can be used so that zero is spin up and one is spin down. So now onto some no-go theorems. So we start with Bell's theorem. So we've kind of already set the scene for this by talking about entanglements. We have this idea that we can have two systems that become quantum entangled and then we take them for a part and then we do some measurements. And we've mentioned that there's these local hidden variable models or a particular model

for trying to save the intuitive aspect of locality and what is usually called local realism in terms of interquantum theory. What Bell's theorem does is rule out these local local variable models by giving us a setting where we can actually experimentally test aspects of how quantum systems behave and rule out these models. So what I'm going to do is kind of explain the setting and what happens when we do this kind of experiment with quantum systems and then how this relates to these local hidden variable models and actually rules them up. So the setting is that we have this entangled pair of qubits and we take them far apart.

We take them so far apart that their space lags are operated, which means light doesn't have time to get from one to the other in the time that we're going to do measurements on them. So it's kind of making sure that there can be no influences being passed between them. And we give one to say Alice and the other to Bob. And then I mentioned that there are these two properties that we can measure of quantum systems that are related by Heiser-Berg's assertive principle. So when we measure one of them, we become maximally uncertain about the other. And I'm going to denote these properties, one by measuring the X observable and one by measuring the Z observable.

And the details of what those measurements are doesn't matter too much. You could think of it as like the relationship between measuring position and measuring momentum. So that's the kind of common example of Heisenberg's assertive principle is that when you measure position precisely, you're uncertain about momentum. When you measure momentum precisely, you're uncertain about position. And these X observables and Z observables are kind of a neat quantum computing way of thinking about what you're measuring on qubits. But you could think of it as the kind of quantum information version of these physical properties of momentum

and position being related by an uncertainty principle. Okay, so what's happening in this experiment here? What happens in this experiment is that Alice has a choice. She can either measure X or Z in the same way that in our fault experiment earlier, we could either measure the size or the color of the socks. And whichever one she measures, she'll get one of two outcomes. We can denote these by plus one or minus one. So if she measures X on her cubit, she'll get plus one or minus one on her measurement

device and she'll get one of those outcomes if she measures z. And similarly with Bob, he can also measure x or measure z on his qubit. And they can each independently decide which of these two properties they choose to measure. And they do this lots of times, then they compare what results they get when they do these measurements of these two properties when they run this experiment lots of times, keep creating these entangled pairs, both do a measurement, both choose which property they're going to measure, and then repeat. I like to represent this using this quantum circuit notation to kind of see what's going on in quantum computing terms.

So in terms of qubits, one way of representing this is that we have Alice and Bob in this, well their entangled pair of qubits is in this state, zero zero plus one one. So this is the entangled state. And then we send one qubit over to Alice, one qubit over to Bob, and then the measurement can be X or Z. They're the options that they have for measurement. And I've also kind of included here kind of just for clarity of how you'd actually prepare something like this in the lab, this is how you'd prepare the

setup, so this is what I mentioned before when introducing the quantum gates is that we have this Hadamard gate is the one that creates suposition on this first qubit. Then we have this control-nop gate, so that's the one that creates the entanglement once we have suposition on this one. So these two together then prepare this entangled state. And then we have this kind of option of whether we measure the X or the Z. And it turns out that the way you can measure X is by essentially doing what you do if you are going to measure Z, but plus an extra quantum gate, hadlock gate in between before you do the measurement. So this is how you'd physically do it when you decide to measure x, you add in this extra gate.

If you're not going to measure it, you take it away. When you do this experiment lots of times, you can compute a certain quantity. You look at cases where they both measure the z property, Alice and Bob, they both measure the x property. Alice measures z and Bob measures x and Alice measures x and Bob measures z. So these are the four combinations of properties that they could measure. You do this lots of times and then you take an average of the product of the outcomes that they got. So each time they got either this plus one or this minus one. And so after you get lots of types and you

take the average of the products of what they got, then you can calculate these kind of averages. So they are called expectation values and you kind of work out these averages of when they measured these different combinations of properties. What Bell's theorem involves in particular, this setup I'm describing is the CHSH inequality, which is another way of showing the results of Bell's theorem, which was a few years later. This is kind of how we're going to see a difference between what local hidden variable models predict and what actually happens with quantum mechanics. So the idea of a local hidden variable model is to say that there's some property that is going to determine what the measurement outcome of the qubits are, whichever property

of these uncertainty-related properties are, there's some kind of underlying variable deciding, making sure that they're the same every time they're both measured. And so it's the kind of idea that there's something that when they were prepared, they got to share this, this variable, this hidden variable, which we've not detected, but we're going to conjecture that it's there. Then we move them apart and this variable is going to make sure that they're the same. So there's this hidden part of quantum addition to quantum mechanics, part of underlying reality that's going to make sure that they're always the same. So there was a time where people thought that thinking about whether this could actually be the

case or not was just a philosophical question that we can't know if this is the kind of model describing reality or not, it's just philosophy. And what Bell's theorem showed is that actually there's an empirical difference between if that is the underlying reality and if there isn't such a variable and somehow the particles don't have this variable that's told them to always be the same whichever one is measured. And it turns out that if you do the calculation of this property using a local hitter variable model, so you assume that there is this kind of variable connecting the entangled systems, then you can show that this quantity has to always be less than or equal to two. So this puts a bound on the outcomes that you can get when

you do this experiment lots of times. And it turns out that according to quantum mechanics, the outcome of doing this is actually two root two, which is bigger than two. And so it violates the inequality. So the idea with Bell's theorem is that if you can actually verify that quantum mechanics really does give a value higher than two when you, by actually doing this experiment, then you've ruled out the possibility of having this local hidden variable model to describe what's happening in Bell's theorem. Great. Now, would it take us off course to talk about how was this inequality derived? Because people would think, okay, there's a variety of expressions I could come up with

with different expectation values, any polynomial or any sort of expression. How am I supposed to understand that this is what we're supposed to measure in the lab as being greater than two in order to demonstrate non-locality or no hidden variables? Yes, good question. Yeah. I mean, I guess I don't know the historical motivation in a way of how this particular form was found. But I guess the aim is what combination of these measurement outcomes can I put together such that the local hidden variable model bound gives me something that the quantum mechanics bound exceeds. And this is kind of one example of how to do that, but there's lots of other ways that

you can also put these quantities together or similar ones. So, um. So this is one instantiation of Bell's inequalities and it's called the CHSH inequality. Mm-hmm. Yeah. Yeah. But it is part of a kind of bigger family of inequalities and that's been a big kind of area since Bell's theorem was proposed is figuring out all the different ways, kind

of characterizing the full space of how you can put these things together, such that it causes a violation and looking at the cases where it doesn't cause a violation. Matthew 10.00 Understood. Ange 1.00 Cool. So now I wanted to talk a bit about what do we do now. Once we've got Bell's theorem, it's told us it's ruled out these local hidden variable models, which were one way of trying to ground quantum physics back into intuition by saying, okay, we have this way of knowing how these particles got to be so correlated. And the way that this is usually presented is that Bell's theorem violates local realism. So that's kind of got these two parts. One is locality, which is the idea that you can't have any influences from one

system to another if they're separated. So something has to physically pass between two things if they're going to be affected by each other. And there's this idea of realism and the kind of way that gets expressed when people are worrying that quantum mechanics doesn't have. Realism is the idea of a system having some definite fixed state before it's measured. But I'll also say that there are lots of different ways of interpreting what locality is and what realism is and people using them in different ways ends up causing a lot of confusion in the, even in the kind of research community. So it's something to always be careful about when someone is making a certain

claim about local realism is to check what they mean by local, what they mean by realism. Can you outline one different way of understanding what locality is and what realism is? So what aspect? So what aspect? So some people like to focus on causation. So they'll define locality in terms of, or at least a form of locality in terms of causation and saying if this system can't cause anything to happen to this system, then that is a local theory.

Another might be in terms of faster the information traveling, faster than light to say as long as information can't travel faster than light between them, then things are local. There's another idea of whether any influence at all could go from one system to another. Because you could imagine that doing something to one system has some physical influence on the other system, even though it doesn't pass information. It can't be used to transmit information. And so a kind of conceptual example where that can happen is in terms of thinking about

wave friction collapse, that this idea that something is kind of collapsing globally is that you could imagine these two systems, maybe something is in sub-position in two different positions and then you look at it over here and it instantly collapses over here, then even though that can't be used to send information, there's something kind of non-local happening. Yes. And there's another kind of property of locality that I think some people find more important than others. I think it's something that Einstein was thinking about and it's a property called separability,

which is about whether kind of the whole is the sum of the parts or not. So can you fully describe two quantum systems individually? And then if you have the individual information about both of them, be able to describe their overall state kind of in a complete way. I find that one very interesting because a lot of people would say that quantum theory doesn't have this separability property, that the whole is more than the sum of the parts for entangled systems in that sense, in that there's information you can get from the two together from the global state that you can't get from the individual local states.

But interestingly, I found out during, when I started doing my PhD research, working with my research group, that there is a fully separable description of quantum theory. So that's something which I then became really interested in because it was really satisfying that you, by shifting how you explain, well, it's essentially by using the realism part. So that's kind of what I tried to mention in this example, which I could talk a bit about is this idea that if you shift what you're counting as your physical system of what quantum mechanics is telling you is your part of reality, then you can get this kind of fully separable local description in the sense that each system does give you complete information about what's happening to that system. And

it tells you everything about what you'll get when you bring them together as well. Yeah, so I think these issues about shifting the definition of realism and locality kind of become clearer with thinking about what different interpretations of quantum theory say, like how they try and make sense of Bell's theorem. I put some examples here. The one I was just talking about is in this setting of Everettian quantum theory. The principle behind Everettian quantum theory is that you treat your measurement device as a quantum system. So you apply quantum theory universally to all scales, including measurement devices. And this has the consequence that those measurement devices, when they measure a system in superposition,

they enter an entangled superposition. So it's often called the many worlds theory because there's this kind of emergent multiverse of you having seen both outcomes when you do a measurement. Often it's motivated by solving the problem of measurement, by resolving the measurement problem, by saying measurement is the creation of entanglement between a measure and the system is measuring. But a kind of interesting independent motivation for it is actually saving locality or saving local realism in the sense that it gives an account where you can have local realism in a way that's consistent with Bell's theorem.

And the idea behind this account is that it doesn't use a local variable model, so it doesn't use one of these models that's been ruled out. Instead, the idea is that you shift kind of your fundamental object that's real. So, there's this terminology of like C numbers and two numbers, like classical and quantum. And the idea is that you kind of shift from describing reality in terms of real numbers to matrices. That's the kind of mathematical way of putting it. But informally, the idea is that you kind of have to shift your physically real fundamental bits of reality to be these multiversal objects that include this fully quantum

measurement device if you've got measurements involved. When you do include that, then you can have a kind of fully local account of quantum theory, but it's kind of shifting to this other description of what the real state is. That's different to how a local hidden variable model tries to complete what a real state is by saying that this hidden variable is kind of determining the real state of affairs. Yeah, and I also included the way that some other accounts of quantum theory, some interpretations get around what Bell's theorem tells us. So there's an approach called the De Broglie-Bohm theory or pilot wave approach. It's kind of based on this idea that there's

a guiding wave that tells particles how to move and so it's a single world interpretation of quantum mechanics. And this drops this kind of strict version of locality in the sense that it allows for some kind of non-local influences to happen. So in that sense, it's got non-locality, which some people would find unsatisfying to kind of sacrifice that strong physical principle of locality. But it still keeps the kind of no signaling property of quantum mechanics, which is the idea that you can't instantaneously send information via entanglement. So you still can't communicate with entanglement, even with this kind of relaxation of locality. So this is where the kind of different definitions of what locality is kind of become important in actually distinguishing

between these different cases and does it cause a violation with contradicting locality and general relativity to reconcile with gravity? And so De Brogbon theory still hasn't been made relativistic. So that's kind of one challenge is to figure out, given these locality differences, how to get something that is kind of closer to integrating with the theories of relativity. Okay. This would be a great point to talk about statistical independence, perhaps even super

determinism. Yeah. There's a tweet here, when I requested questions for this podcast, where Sabine Hassenfelder asked about why assumes statistical independence. This is useful to define what it is. Okay. Another approach is from super determinism. So this drops an assumption that is not explicitly stated when you say that the assumption is local realism.

It's kind of another assumption, which is often kind of just implicitly assumed because it just makes sense. So it's this idea of measurement independence that came in this. It comes into this thought experiment with Alice and Bob. The idea of measurement independence is that Alice's measurement is independent from Bob's measurement. So they freely choose whether they're going to measure the x property or the z property individually. There's no dependence of what Alice chooses to measure and what Bob chooses to measure.

And by dropping this measurement independence assumption, you could also get this approach to quantum mechanics called super determinism. And the kind of idea of it being super determinism is that in such a world where we don't have these independent choices from Alice and Bob, then it seems that the laws of physics somehow conspired to make everything work out according to the laws of quantum mechanics, but with this kind of carefully arranged dependence of the measurements. So, um, it sounds like you're not a fan of it. Uh, I mean, I guess for me, in terms of my personal feeling is that I find this

local account that I mentioned where we can have these, like these Q numbers, which give this separable account as well. We can fully individually describe individual systems. I find that convincing. So needing to drop locality or dropping measurement independence to me seem not necessary because we can already reconcile locality with quantum theory in this way. So we don't need to sacrifice these like really strong principles. Yeah, it seems to lead to a very strange, strange physics, but I will say that neither of them are something that I've kind of deeply looked at, but that's the reason that I haven't felt motivated to look into whether they can give a satisfying account. So just to wrap up this section, I wanted to give a shout out to another kind of result,

which is, uh, Surilsson's bound, I don't know if I pronounced that correctly. But the idea of this is that it tells you the upper limit on what the violation can be from quantum mechanics in terms of these correlations. So this kind of 2 root 2 is actually the upper limit on how correlated the quantum systems can be via entanglement. And there's an interesting feature that it's not actually the full upper limit that we'd get if we were just trying to satisfy not being able to send information instantaneously via entanglement. So that's this no signaling requirement. It's actually lower than that. So there's a bunch

of research on trying to explore that gap and what would get wrong if it was more powerful or what's the, what's kind of deciding how powerful it is. So let me see if I understand this. Bell's inequality in the CHSH formulation says that something should be less than two if it were classical. It's not. It's greater than two. Namely, it's been measured to be two times the square root of two or calculated to be two times the square root of two. Then you wonder, could it have been five? Could it have been 10? And then this guy, which whose name neither of us can pronounce, but is written on screen here, he says that there is a bound, there is an upper bound.

And then the second question is, okay, this upper bound comes with certain assumptions. So what happens if experimentally we find it to be greater than that? What physical implications would it have? Is that what you're saying? Yeah. Yeah. So, Are you saying that, look, it's lower than that. So what can saturate that bound? Uh, yeah. So saying that the bound tells us that quantum theory, whatever we try and do, however we try and manipulate these expectation values a bit like you were

asking before about how we could come up with a different way of putting them together. Whatever we try and do, we can't get the correlations kind of giving us something so that the bound gets bigger than 2.2. But the physical principle of no communication via entanglement would let us go higher. So that principle isn't kind of the thing stopping quantum mechanics from having more powerful correlations. So that's what creates this question of the physical implications of it having this particular limit. Like it seems kind of a bit random, I guess of why is it at this point? Why is it R2, R2?

Why is it not at the bound given by not being able to communicate using entanglement? So what's the explanation then? I'm not sure we have a good answer. Yeah. Is it an open problem? Yeah, I'd say so. I'd say it's something that motivates a certain research program where people try and kind of, often they kind of have these interesting ways of geometrically looking at these bounds

where you can look at these kind of 3D geometrical versions of the full space of correlations that you could have and then what's kind of carved out by quantum theory and then kind of exploring toy models of like imaginary variations of quantum theory and imaginary theories that would lead to the bounds being higher and then kind of exploring the properties of those. So there's a bunch of work looking at these kind of toy models and what physics they would imply. Um, so there's been a lot of interesting work in that direction, but I don't think there's been a conclusion as to pointing out exactly what the property is that has caused it to

be at this value. Okay. Cool. Um, so now we have GHZ states. So these are named after Greenbeggar, Horn, Salinger. And ultimately what GHZ states show is the same kind of metaphysical conclusion as Bell's theorem. So they're going to rule out local hidden variable models again, but rule it out in a stronger way.

Because we saw with Bell's theorem that we had this inequality, we had to run the experiment loads of times to kind of violate this statistical bound based on averages. With GHZ states, what's cool about them is that you can show the same strength of outcome in terms of ruling out local hidden variable models, but without having to violate a bound, you can just do certain measurements if you get certain outcomes, well, according to quantum mechanics, you will get certain outcomes that will just through kind of one measurement will show you that you've got results that can't be explained with local hidden variable models.

So it's like a stronger version because Bell required repeated measurements, you have to take an expectation value, whereas here you can actually just do one experiment. Yeah. Yeah, exactly. Yeah. So a stronger kind of stronger way of ruling out the same class of theories. And so the setup is kind of similar to Bell in that we've got, but we've got three qubits instead of two or three quantum systems.

So what you do is you get three qubits and you entangle them all together. So we're going to create this state, 000 plus 111. So this is a superposition of all of the three qubits being zero in superposition with all of the three qubits being one. So it's just like our previous 00 plus 11 state, but with an extra qubit. And similarly to Bell, again, we have this option of measuring these two incompatible properties, the ones that are related by Heiseberg's associative principle, the X observable and the z observable. So we have the option of doing each of these two measurements on the three qubits. So what do we find? So here again, I've kind of put out this quantum

circuit depiction of what's going on, of how we'd represent this with qubits. So we have this 0, 0, 0 plus 1, 1, 1 state that we then can measure each qubit as x or z. And here I've kind of broken it down again into how you'd actually prepare it is this had mod c0 like before to get the 0, 0 plus 1, 11, but now we have an additional C not with the third qubit and that's what gets us this 000 plus 111 state. And then we have these possible Hadmod gates that we add to get this X measurement or we don't add them to do the Z measurement. And what we find that if we kind of combine the outcomes of four different combinations of measurements that we do, we get different

predictions depending on if there's a local hidden variable model describing what's happening and if quantum mechanics describes what's happening. So we have these options of getting the plus one or the minus one outcomes and then when we multiply them together, we can either find according to local hidden variable models, they'll give a plus one outcome and according to quantum mechanics, they'll give a minus one outcome. So we have this difference in what the outcome will give us. And so in comparison to Bell, we're rolling out the same class of theories of local hidden variable models, but instead of violating this inequality where it's less than or equal

to two in the Bell case, instead now we have an equality in that we're testing if it's equal to one or if it's equal to minus one. So we're not trying to violate a bound. We're just getting a certain outcome. So in that sense, we call it an all or nothing result in that it either tells us we've ruled them out or it doesn't. There's not like a quantity of violation in the way that there is with Bell. Um, and I wanted to give a shout out again to another theorem that's also related to these theorems. It was proposed, I think a year or two after GHZStates maybe called Hardy's

Paradox or Hardy's Theorem, because it's not really a paradox in the sense that it could be resolved as with all of them, I guess. But the idea of Hardy's paradox is that it's actually kind of in between GHD states and that's the theorem in terms of ruling out local variable models. So it also rules out local variable models, but in such a way that if you get the right combination of measurement outcomes, then you can rule them out. So there's this kind of probabilistic aspect of you may get the outcomes that will rule them out, but you're not violating a statistical bound and you can actually do it with just two qubits.

So that's the kind of advantage over showing it with GUSS states, which need three qubits is that you can do it with two qubits, but then you have this probabilistic aspect. So you can kind of see Bell's theorem, Hardy's paradox, just states as kind of three different ways of ruling out local variable models with kind of increasing strength in the sense of being more deterministic. Great. Now, why is it called a paradox? You just mentioned it was a theorem. Yeah, so it's kind of known as Hardy's paradox because it's similar to the Bell

inequality setting in that what you end up concluding is if Alice measures X and Bob measures Z, then they should get this result. And if you do this kind of classical intuitive reasoning, you end up concluding that if they both measure x, they should get plus one, then you use quantum mechanics and you find that it's minus one. And so you get this, in that sense, it's a paradox because it seems that classical, that what we expect from our intuition leads us to conclude that Alice and Bob will get a different result to what they actually get.

Okay, so to be clear, it's not a paradox in the sense of A and then you also get not A, so an antinomy. It's more that there's an unintuitiveness about quantum mechanics if we were to hold on to classical mechanics as our worldview. I'd say it's a paradox in the sense that you can kind of say, if I use my classical intuition, I get one outcome. If I use quantum mechanics, I get the opposite outcome. So that's your contradiction. But if you then say, ah, the classical intuition was wrong because quantum mechanics doesn't

work like that, then you'd say, well, it's not a paradox. It's just a thought experiment or a theorem that tells me that there's no local hidden variable models. Understood. Yeah. So now we can talk about the Koch and Specker theorem. This is a theorem that was published relatively soon after Bell, I think. It's kind of similar in spirit to Bell, but it rules out a different class of models for quantum theory related

to a property called contextuality. In particular, what we'll see that it rules out is non-contextual hidden variable models in a similar way to how Bell rules out local hidden variable models. Yeah, I just want to kind of introduce this by saying the idea of the spirit for what this theorem shows. The idea is to consider, let's say there's three different properties that we could measure. That's A, B and C. A and B can be measured together simultaneously. That's fine, wait, we can do that. We can measure A and C together simultaneously. A and B kind of don't have this Heisenberg and Saatchi principle type incompatibility, neither do A and C.

But B and C do have this incompatibility, so we can't measure B and C at the same time. Now what this property, non-contextuality, would say is that, okay, we could measure A together with B, or we could measure A together with C. It's not going to make a difference to what the outcome is when we measure A. It doesn't make a difference if we measure it with B or if we measure it with C. So you can think of B and C as being the context in the sense that they are the context in which A is either being measured with B or being measured with C. And so the idea of non-contextuality is that the measurement outcome we get on A doesn't depend on the context. So it doesn't depend on whether it's being measured with B or C. But what we find with

quantum theory is that in this case where B and C have this incompatibility, we do get the phenomenon of contextuality, which means that the outcome that you get from measuring A does depend on whether you measure it together with property B or with property C. So that's the kind of idea of what this contextuality property is. Great. Okay. Now let's be less abstract. Let's be more concrete.

So B and C, maybe you have some slides prepared, but people know that position and momentum don't quote unquote commute. So that potentially could be B and C. I don't know if you have an example in mind. A and B commuting and then A and C commuting. So can you please come up with an example? Yeah. and then A and C commuting. So can you please come up with an example? Yeah, I can't think off the top of my head, the intuitive one in terms of those kind of properties, but I think this can clarify some things.

So this is an implementation of kind of demonstrating this contextuality property is called the Merman--Perez Magic Square. So that's the kind of approach I've used to try and explain what's happening because there are various ways that this could be introduced, but I think this Magic Square is kind of a neat one. The idea is, like before, we have two qubits that we're going to measure. One interesting aspect now compared to Bell is that we're going to measure. One interesting aspect now compared to Bell is that we're not going to assume that they were prepared in a particular state like entangled, they can actually be prepared however you want. But let's just

say we've got two qubits and we're going to measure them. We have three different ways of measuring them. We can measure the X property, the Y property or the Z property. And for something more visual, you can imagine if you think back to the sphere describing the qubit, one way of thinking about these different properties we measure are is like measuring along the X, Z, and Y axes of the sphere. So the Z axis is the one that projects it into 0 or 1. The X axis would actually project it into a superposition state on either side of the sphere and measuring of the y-axis would project it onto these superposition states on the other sides of the sphere.

And you can also think of this in terms of spin as when you have certain particles they can have spin in these three different directions in some sense. You can have the z spin, the x spin and the y spin. These properties are all mutually incompatible in the sense that they've all got this Heiseberg's uncertainty principle connection in that the x and z spin have to be uncertain with each other, z and y spin, the y and x spin, so they all have this incompatibility together with each other. What we want to look at is a situation where we have compatibility. Looking at this square, so here we have z2, which means z property on the second qubit.

Here we have x1, so that's x property on the first qubit. And then we have x1, z2. Yeah, so we can measure z2, x1, or x1, z2, is this kind of jointly measuring x on this qubit and z on this qubit. And these three, all of them are compatible with each other so we can measure them together. They're compatible. And that's true of all of the entries of all of the columns. So these three are compatible and these three are compatible. Are you sure about that?

Actually, sorry, that stopped the case. This is one where they're not compatible is this column. this column. So, the third column, this z1, z2, x1, x2, y1, y2, they're actually incompatible. Each row has three elements which are compatible. The z1, the z2, and the z1, z2 cannot be measured simultaneously. The same with these three, and the same with these three and the same with these three. So this is what gives us these, we get the plus one is indicating that the column is compatible or the row and the minus one that it's not compatible. And then the question we want to ask is, is there a way that we can assign this kind of plus one or minus one value to each of these elements so that when we times them together, it reproduces what we get here. So there's a way of assigning plus one and minus one to these elements in order

to reproduce these values. And so what you can do is kind of try and fill in this square like a puzzle, try and see if there's a combination of plus one and minus one that you can put so that when you multiply them, it'll give you these outcomes. And it turns out that there isn't a way of doing that and that there's no consistent way of labeling them with plus one and minus one. That is indicating that these properties have this property of contextuality in that there isn't a way of them kind of having this independent value and that telling you what's going to happen when you jointly measure these properties alongside each other.

Okay. Yeah, so the kind of conclusion from this is that since you can't assign this plus one and minus one to all of these properties, it rules out a certain class of theories that would explain this kind of property in terms of non-contextual hidden variables. This rules out this class of theories and tells us that actually there's this kind of fundamental contextuality in the sense that it matters what we're jointly measuring with a property. Yes.

There's some interesting comparisons with Bell. So one that I mentioned is that in this case, it's not a state dependent result in that. We've just looked at how we're measuring it, like what properties we're measuring. We've not talked about what state the particles were actually in. So that's quite nice because we're not just looking at a property of entanglement or a special state here. We're just saying in general, whatever state these were in, if we do these measurements, then we're going to get this property. So that's a nice aspect of this theorem.

And another nice aspect is that we've mentioned that with Bell's theorem, you have this space-like separation needed, which is what ensures that the systems can in no way influence each other from some kind of below-light speed influence. In this case, we've not said anything about locality, so that's what's meant that we've not said anything about. We don't require this kind of space-like separation being four apart to draw these conclusions. So we can, we can rule out these non-contextual hidden variable models without having space-like separation. So in that sense, it's kind of easier to get out of loopholes in terms of ruling

out this class of, of models for quantum theory. What I like about your explanation is that ordinarily people should know quantum contextuality as they can tell is highly specific and it's usually said that quantum contextuality means that your measurements depend on what settings you use to measure them. And then you're like, well, why isn't that obvious? Because as you mentioned, we have the Heisenberg uncertainty principle. So what you do subsequently depends on what just occurred or what you just measured prior.

And then you also have the Stern-Gerlach experiment, which will always measure a spin up or spin down, no matter how you rotate it. So isn't it obvious that what the measurement is depends on what you measure? And that's why that phrasing, quantum contextuality, rotated. So isn't it obvious that what the measurement is depends on what you measure? And that's why that phrasing, quantum contextuality equals your measurements, depending on what you use to measure, is misleading. And this magic square demonstration is much more clear.

Yeah. And it's, yeah, because there's kind of this idea of what are you measuring with. So that's kind of what comes with this picture is this incompatibility sneaks in, even when you think you're measuring with compatible. You've made sure that what you're measuring with is compatible, but because those things themselves are incompatible, that's seeped into your measurements and you can't assign this fixed value to this property anymore. So it's that kind of assigning of a fixed value, which is where this kind of hidden variable aspect comes in, but with the contextual aspect instead of

local. Okay, so you've just got a whirlwind tour of quantum mechanics and quantum computing and no-go theorems and the related concepts and terminology. Because we're going to keep this to under two hours, what Maria is going to do is just go over the rest of her presentation quickly because there will be a part two where Maria will explain rather than quickly in depth what she's about to give an overview of. And if you have any questions about what just occurred or what is coming up, then please leave them in the comments. What's coming up? We're going to talk about the Legate-Gaug inequalities. So these relate

to measuring the property of a system over time to test an aspect called macro realism, so kind of to test definite states of macroscopic systems. We'll talk about the PBR theorem as well, which is testing whether the wave function is a physical property of a quantum system or whether it's just information about a probability distribution. I'll also do a bit of a summary of what all these different Nogotheriums have told us and my personal outlook on what it's told us, what's coming with future Nogotheriums or other ones people are working on and a perspective from the Everettian theory of quantum mechanics on how to resolve them all. Also, how people are trying to modify these to further test aspects such as quantumness

of gravity. And that's what's coming up. Wonderful. Thank you so much, Maria. I should shout out Jim O'Shaughnessy because you and I, we both met from the O'Shaughnessy Ventures. We were both granted grants from that organization. And so thank you, Jim. And it was lovely meeting you and talking with you behind the scenes, Maria. Yeah. Thanks for having me.

And thanks to Jim as well for connecting us and look forward to talking more about these ideas next time. New update! Start at a sub stack. Writings on there are currently about language and ill-defined concepts as well as some other mathematical details. Much more being written there. This is content that isn't anywhere else. It's not on theories of everything. It's not on Patreon. Also, full transcripts will be placed there at some point in the future. Several people ask me, hey Kurt, you've spoken to so many people in the fields of theoretical physics, philosophy, and consciousness. What are your thoughts? While I remain impartial in interviews, this substack is a way to peer into my present deliberations on these topics.

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