I am not familiar with that, but the key result to always keep in mind is that ultimately all of quantum mechanics is a limit of quantum field theory, and quantum field theory is manifestly causal and relativistically invariant. So no instantaneous causing of anything. Causality is always inside the light cone. Anything that “instantaneously is caused by one object has another frame of reference where the second object causes it, so the only valid conclusion is neither does (this is the relativity of simultaneity, essentially).

Thanks! And that's great! More content along these lines would be awesome, I've not seen any explanations of it other than in research papers and research talks. Chiara Marletto gave a nice talk about the local quantum formulation and applying it to the Aharonov-Bohm effect for Oxford Quantum Information Society, perhaps that's where you saw it? kzfaq.info/get/bejne/orlpm5WfvMjFomw.htmlsi=KA9XRZaZNIRQcO4Y It's actually from Chiara that I first found out about the fully local explanation for entanglement, when I started working with her for my master's project! It's a shame it's not discussed in standard quantum courses.

Glad you enjoyed the paper! A pair of entangled qubits in the state |00> + |11> will always give the same outcome when measured in the same basis, and an entangled pair |01>+|10> will always give opposite outcomes. The parameters θ and φ in the paper vary the X-rotations applied to each qubit, so depending on those, the entangled pair could be |00> + |11>, |01>+|10> or in another entangled state. As an example, consider θ = φ = 0, so the entangled pair is never modified from its original state of |00> + |11>. Then in eq. 38, the expectation value of z_1 = 1, indicating that the measurement outcomes are always the same. Hope that helps!

Good to hear you're enjoying the videos and running the circuits! Yes I didn't actually run the circuits using a simulator in this video, as I didn't feel it was essential for the explanation, but I very much encourage you to play with and run the circuits yourselves to see the outcomes! For example, at the circuit at 4:47, you could try varying the parameters in the parameterised gates to check that whenever the qubits are measured in the same basis, they give the same outcome. You could also add a measurement on the check qubit of the circuit at 12:05. Again you'd see that whenever the parameters in the gates are the same (so the qubits are measured in the same basis) the check qubit always gives an outcome of 0. :)

@@maria_violaris thanks for suggesting to play with same versus different basis. Would you mind writing the qc.run instructions in github repository. I tried to run but, because of limited experience with simulator and library, I got some errors and run failed. It is always nice to see run succeed, especially on real hardware.

By determined, do you mean that we learn what it is at a certain point in time, or are you saying the other particle suddenly conforms based on our measurement? Either way, yes simultaneity is relative but you can account for that. You can choose a reference point and unpack the things that cause the disparity and can be sure you are checking at the same moment.

@JundArbiter You mean every observer observes particles' states being determined simultaneously? The fact that this doesn't contradict other laws is surprising.

@@user-mq8hg4pj4b The fact that we know time is relative is a kind of why you can do it. those reasons why things are relative and how exactly they're relative are just equations that you can work backwards. if you put the entangled particle with someone in a spaceship moving at almost the speed of light going at some random angle, you could still determine a time that something happens. I think the farthest this experiment has been done is 14 km and I could be wrong about that but I think it was a Chinese experiment

@JundArbiter I wish I could see the equations that explain why it doesn't contradict relativity theory. It is hard to understand with words only.

@@user-mq8hg4pj4b As long as the moment is determined by someone in the same reference frame it isnt important what the two points are. Another reference frame might determine that the moment was different but still that it was the same moment. The more similar those reference frames are though, and the more certainty you have about whats going on in each, the closer those two determinations will be

Hi, glad you found it interesting & well presented! Thanks for the feedback about moving from the Heisenberg picture explanation to the information flow in the quantum circuit. The overall idea is that, by tracking the Heisenberg observables of individual quantum systems at each stage of the quantum circuit, you can see that information only gets transferred from one system to another via direct interactions. Only direct gates, such as the CNOT gate, enable information from one quantum system to appear in the observable in the other quantum system. I definitely skimmed over the details there in the video, to avoid making it too long and technical, though I tried to convey the flavour of how locality can be made explicit using the Heisenberg picture. A more detailed explanation of how to track info flow is a great idea for future content, but for now I will refer those that want the mathematical details to the papers linked in the description. In terms of locality, there is indeed lots of different uses of the term locality within quantum theory and other fields which can get confusing. The important aspect here is that the aspect of quantum information theory that everyone unanimously agrees on is that it obeys no-signalling, i.e. changing one quantum system cannot instantaneously have an observable effect on a distant quantum system, even if they are entangled. (This is an even stronger constraint than no-faster-than-light communication, as it doesn't explicitly say anything about light-speed). Einstein's local realism is a stronger constraint than that. It forbids changing one system having any instantaneous effect on a distant region of space, even an unobservable effect. If changing one system could have instantaneous but unobservable effects on a distant system, that would make it more difficult to reconcile with general relativity. Fortunately, we can see explicitly using the Heisenberg picture that quantum theory does not admit any effects to be transported at a distance, and every region of space has a fully local description that doesn't depend on systems it is spatially separated from.

A deeper dive into different levels of "locality", their physical implications and which theories obey them could also be a fun topic for future content :)

@@maria_violaris Thanks for the detailed explanation. And I agree the many variations of locality would be a very fun topic to discuss. I guess what is particularly confusing at times is how different communities in theoretical physics take for granted their own definitions haha. All the HEP theorists are very satisfied with microcausality as the only "locality" important in QFT and then some people of IT from QUBIT came along recently and were all like we can show that it is not impossible but merely costly in terms of complexity to break causality, that's the reason why you dont observe non-causal things. I hope videos and scicomm by people like you reach people in HEP communities and they for once take seriously, the basic problems of definitions pointed out by quantum foundations. Its pretty frustrating the lack of intercommunication (having myself been in both communities lol).

Also I understand that it will require reading of the papers to really understand how the heisenberg formalism plays a role here. Thanks for the references !

GHZ states can be used to demonstrate Bell non-locality, in a "stronger" way to the standard Bell test in the sense that GHZ Bell-nonlocality is deterministic and does not depend on inequalities. Like the Bell test with an entangled pair of qubits, the GHZ state test rules out *local hidden variable models*. The approach I give in the video, where quantum mechanics is explicitly local using the Heisenberg picture, is not a local hidden variable model, and hence is not ruled out by the GHZ test any more than it is ruled out by the violation of Bell inequalities with an entangled pair of qubits. Incidentally, Hardy's paradox (which I cover in another video: kzfaq.info/get/bejne/obKUqad1rbLaf3U.htmlsi=hrf9vN_IZEc20IdB) also demonstrates that quantum theory cannot have a local hidden variable model, in an intermediate way: it only uses 2 qubits, not 3 like the GHZ test, but also doesn't depend on violating inequalities (though it does require post-selection). Tl;dr: the GHZ test rules out local hidden variable models, like violating Bell inequalities with an entangled pair does. These models are not the only local theories possible. In the video I explain how the locality of quantum theory, made explicit in the Heisenberg picture, is fully consistent with Einstein's local realism and the results of quantum experiments.

ok so heres what youre gunna wanna do: 1. Design your Qubits Choose Qubit Type: Superconducting qubits are commonly used, like transmon qubits, flux qubits, or phase qubits. Circuit Design: Design the superconducting circuits that will function as qubits. This involves careful planning of the circuit layout, including Josephson junctions, capacitors, inductors and the resonators. 2. Fabrication of Qubits Materials Selection: Choose materials with good superconducting properties at low temperatures. Nanofabrication: Using techniques like electron-beam lithography, create the designed circuits on a substrate. This process requires a clean room environment and precise control. 3. Creating the Quantum Processor Integrating Qubits: Connect multiple qubits to form a quantum processor. This includes designing and implementing a quantum bus for qubit interactions. Control Lines: Add control lines for each qubit, enabling manipulation of their states through microwave pulses. 4. Cryogenic Environment Cooling System: Superconducting qubits require extremely low temperatures to operate. Set up a dilution refrigerator that can cool the quantum processor to millikelvin temperatures. 5. Control and Measurement Electronics Microwave Pulse Generation: Implement electronics to generate precise microwave pulses for qubit manipulation. Readout Mechanism: Design a system to measure the state of the qubits, typically involving resonators coupled to the qubits and connected to measurement electronics. 6. Software and Quantum Algorithms Programming Interface: Develop or utilize a quantum programming language and interface to create quantum algorithms. Algorithm Implementation: Implement algorithms tailored for quantum computing, like quantum Fourier transform, Grover's algorithm, or custom algorithms based on the intended application. 7. Testing and Calibration Calibrate Qubits: Perform extensive calibration to fine-tune the control and measurement of qubit states. Benchmarking: Test the system's performance using quantum computing benchmarks to evaluate aspects like fidelity, coherence times, and error rates. 8. Integration and Scaling System Integration: Integrate the quantum processor with classical computing resources for control and data processing. Scalability Considerations: Plan for scalability, both in terms of increasing qubit count and improving error rates. Important Considerations Cost and Resources: youre going to need a lot of $$$ hope this helps!!

@@qiskit let see 🙈

I am not sure I really follow the locality argument of this demonstration, because there really is no spatial aspect in the quantum computer. They key point to remember is that entangled states do not communicate the results of “an earlier measurement” to tell the other qubit how to behave. Entangled states have correlations. Regardless of any order of the measurement of the qubits, or spatial separation, you always see the correlation. There is no need for any communication between the qubits. While the quantum formalism makes it very clear what the results of the measurements will be and how you will observe the correlations, it says nothing about how quantum objects carry out this “dance” to produce these results. It is not knowing how, that often bothers people. But it is very similar to asking the question, which slit did the particle go through in a two-slit experiment. Most do not like the answer it cannot be determined, even though that is the best we can say. I would say the check qubit circuits simply are directly sensitive to the correlations, rather than the individual measurements, so measuring the check qubit has simple results, with no controversy (achieved by either additional entanglement in the deferred measurement case, or by copying classical information in the measured case). Diego, do you think you can send me an email. Really want to discuss your project with you.

In what sense do you find it naively simplistic? Happy to address any specific questions you have about how quantum theory is explicitly local in the Heisenberg picture and therefore in the EPR paradox. If the problem is more that it seems generally "too simple" or "too good to be true", here's some points to consider: 1) It's not trivial to see that the local observables of each subsystem must provide local and complete information about the global system; it had to be proven and relies on mathematical properties of observables in quantum theory where they obey very strict constraints. So there's underlying mathematical properties of quantum theory doing the work in the background to ensure the local formulation all really checks out. 2) The local formulation doesn't make the EPR paradox trivial or meaningless, it just changes the conclusion about what the thought experiment and Bell's theorem demonstrate. They don't demonstrate that quantum theory is non-local; they demonstrate that our physical elements of reality are not described by numbers ("c-numbers") but by matrices ("q-numbers"). 3) The local formulation really does provide neat, consistent explanations of the flow of information in the EPR paradox and other thought experiments, while maintaining consistency with core principles of physics like local realism. It's not surprising or problematic if a good explanation seems neater and simpler than previous ones - it's a sign that it's a good explanation!

@@quantum4everyone "because there really is no spatial aspect in the quantum computer" Indeed when the quantum circuit I present is implemented on a single quantum computer, the qubits are not distantly separated in space. However exactly the same quantum circuit describes the situation where Alice and Bob's qubits are distantly separated in space. The point of the quantum computing demonstration here is to illustrate the idea of the thought experiment, though it doesn't implement the real thought experiment (that would need quantum networking, e.g. having some distant qubits connected by an optical fibre that can be used to entangle them). "I would say the check qubit circuits simply are directly sensitive to the correlations, rather than the individual measurements, so measuring the check qubit has simple results, with no controversy" Having the check qubits sensitive to only a global property, the correlations, that is not a local property of each individual subsystem, violates local realism. That's why the existence of an explicitly local formulation is important, as it shows that quantum theory has a local and complete description. A bonus is that we can then track the local flow of information in e.g. the EPR paradox and (in next week's video) the quantum teleportation protocol.

@@maria_violaris I think you have to work harder to try to have a convincing argument that the Bohm variant of EPR, carried out on spatially separated qubits that are measured by space-like separated detectors is a local measurement. I cannot see how it ever is using usual definitions of locality. The fact that a local variant gets the same results as a spatially separated one is not the same as saying the spatially separated one is local. As for the check qubit being sensitive to only the correlations, that is exactly what it is set up to do. It is 1 if they are correlated as prepared, and 0 if not, I don't understand the objection. In any case the Bell experiments show quantum mechanics cannot be a local realism theory, so violating local realism is perfectly fine as this is what quantum mechanics does. I still do not follow what point you are trying to make. Are you saying the Aspect experiments do not show local realism is not tenable?

​​​@@maria_violarisWell, the way in which the EPR paradox is addressed in this video seems to me like a desperate attempt to try to restore a bit of classical intuition to quantum phenomena (entanglement). In my opinion, the Epr paradox is telling us something really deep about the functioning of the cosmos. I do not see it as correct to affirm that the paradox has been "resolved." Because I consider that the mystery still persists, I think I resonate more with the way in which Professor "Leonard Susskind" addresses this paradox, and it seems to me that the ER=EPR conjecture lays the foundations to finally aspire to "understand" the underlying mechanism involved in quamtum entaglement In any case, under no circumstances would I dare to say that the paradox has been "resolved."