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# Tag Info

Accepted

• 1,631
Accepted

### Simultaneous eigenstate of commuting observables and their tensor product

Measuring an observable does not mean applying the observable operator to a quantum state but rather measuring the state in the eigenbasis of the operator. A measurement will basically produce an ...
• 17.7k
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### Formal proof of Bell's inequality in CHSH form

I want to emphasize that you are wasting your time with this historical stuff. But since you insist I'll answer anyway. First of all, note that the inequality \left|\int d\lambda p(\...
• 2,833
Accepted

### What is the no-signaling set and how can it be related to other types of correlations?

I'll describe the case of two party correlations but this can straightforwardly extended to more parties. Let's give a box to Alice and a box to Bob. Alice and Bob can interact with their boxes by ...
• 5,988

### How is Bell’s Inequality converted to the CHSH inequality?

... and the question changes again. Re Update 4: I'm not sure what you intended the variable $a$ to be in the question (I think part of the problem is that you've got muddled between the chosen ...
• 60.2k

### Determining whether $P(ab|xy)$ factorizes in Bell experiments

I think you're doing things a little bit backwards. You probably shouldn't be calculating $P(a|x)$ or $P(b|y)$ in advance, because you're simply trying to ask: Given a set of $\{P(ab|xy)\}$, do ...
• 60.2k
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### Why only one of the qubits is rotated in the CHSH circuit?

In an actual implementation of the CHSH game, both Alice and Bob must conditionally rotate their qubit. If one of them doesn't do any conditional operations to the qubit, then all the actions to the ...
• 40.1k
Accepted

### Is it advantageous for a state to have higher Bell CHSH violation?

Yes, the CHSH game/scenario is an example of a robust self-test. What this means is that if you obtain a value that is close to the optimal Bell violation, then the state $\hat{\rho}$ and the ...
• 2,111

### Projecting $\lvert ++ \rangle$ on Bell Basis

The four Bell states are $$|\Phi_{\pm}\rangle=(|00\rangle\pm|11\rangle)/\sqrt{2}\qquad |\Psi_{\pm}\rangle=(|01\rangle\pm|10\rangle)/\sqrt{2}.$$ So, let's consider what happens then we try and ...
• 60.2k

### How to prepare an arbitrary two-qubit state?

First of all, I'm assuming you mean the state : $\alpha \left|00\right> + \beta \left|01\right> + \gamma\left|10\right> + \eta \left|11\right>$. What you actually want to do is to act with ...
• 131
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### Find the Bell States of A and B in the following scenario

Simply start by writing out everything $$|B_{00}\rangle_{13}|B_{00}\rangle_{24}=\frac12\left(|00\rangle_{13}|00\rangle_{24}+|00\rangle|11\rangle+|11\rangle|00\rangle+|11\rangle|11\rangle\right)$$ ...
• 60.2k

### Are there Bell-like violations that can be observed without collecting statistics?

Yes, there are. I just wrote a paper about it, actually. You need to define carefully what you mean by obtaining a Bell violation or ruling out local hidden variables. You can't demand to have a ...
• 2,833

### Are there Bell-like violations that can be observed without collecting statistics?

I believe you're thinking of the all-versus-nothing proofs based on GHZ states. You start with a state such as $$|\Psi\rangle=\frac{1}{\sqrt{2}}(|000\rangle+|111\rangle)$$ and you select at random ...
• 60.2k
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### Are there Bell-like violations that can be observed without collecting statistics?

Are there scenarios in which Bell nonlocality can be observed without such averages, that is, in a single-shot scenario? No, you have to collect statistics. Any single result you see could have been ...
• 40.1k

### References examining Bell inequality violations at large distances

The largest scale Bell test done thus far is the "Cosmic Bell Test" of 2017. It ruled out hidden variables within a distance of 600 light years from Earth. The 16 significant Bell test experiments ...

### In Bell's inequalities, what is the meaning of assuming that the physical properties $P_Q,P_R,P_S,P_T$ have definite values?

This, in a nutshell, is the whole issue of quantum. You say "of course an electron will have either spin up or spin down". It might seem like it should, but this is founded purely on your ...
• 60.2k

### What are the 2022 Nobel Prize winning papers of Alain Aspect, John Clauser, and Anton Zeilinger, and how do they fit into the timeline of QIS?

Well, a sidebar in Quanta magazine's article had already created a nice timeline on the experiments and events leading up to the 2022 Nobel Prize in physics. Also as identified by @Rammus in a comment,...
Accepted

### Why is $P(1,2)_{\text{same}} = \frac{1}{4}$ and not $\frac{1}{2}$ in Preskill's Bell experiment?

I do understand that the sum of these three probabilities is greater than one because there are some constraints already involved; like if we uncover all three coins at least two have to be the ...
• 60.2k
Accepted

First, is this value correct? Yes, it is. If you expand out the calculation you're doing, this is the same as $$\sqrt{2}\langle\psi|X\otimes X+Z\otimes Z|\psi\rangle$$ for any two-qubit state $|\... • 60.2k 2 votes Accepted ### What are the two measurements per box being done in the Bell Tests in the IBM Quantum Experience "Entanglement and Bell tests" Section Both$A$and$A'$measure the same qubit, while$B$and$B'$are applied to the second qubit. Alice chooses (randomly) which of the two measurement settings ($A$or$A'$) she will choose for each run ... • 2,457 2 votes Accepted ### Why is the CHSH inequality defined with a minus sign? Imagine you had a general formula $$C=a_1QS+a_2RS+a_3RT+a_4QT.$$ Algebraically, we know that if$Q$,$S$,$R$and$T$are random variables with values$\pm 1$, then each term such as$QS\in\{\pm 1\}$... • 60.2k 2 votes Accepted ### Problem about entanglement swapping I guess the way that I'd start (aside from just getting a computer to do it!) is to remember that the Bell states form an orthonormal basis. So, you can ask, for example, about what the$|\Phi^+\...
• 60.2k

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