11
votes
Accepted
Are correlations stronger than those allowed by quantum mechanics possible?
Yes, it is possible to conceive theories with "stronger correlations" than those given by quantum mechanics.
One way to make this statement precise is to consider some kind of "measurement apparatus" ...
glS♦
- 26.3k
9
votes
Is it true to say that one qubit in an entangled state can instantaneously affect all others?
If Alice and Bob have an entangled pair of qubits and Alice locally measures her qubit, it does not affect local state of the Bob's qubit in any way. Mathematically, if Alice measures but does not ...
- 3,244
8
votes
Is it true to say that one qubit in an entangled state can instantaneously affect all others?
It is certainly true that, within the mathematical description of qubits, operations on one qubit can require the whole description to be updated. This therefore affects the description of every qubit....
- 11.4k
8
votes
Accepted
What is the relationship between the Toffoli gate and the Popescu-Rohrlich box?
A natural way to relate Toffoli gates and PR boxes is to see them both as representations of the AND function of two binary inputs, but in different ways. The connection with the AND function is ...
- 6,227
6
votes
How would a Quantum Computer (network) perform loophole-free Bell tests?
When people talk about a loophole free Bell test, what they really mean is that the two loopholes that most concern the majority of people are closed simultaneously: the measurement loophole and the ...
- 60.7k
6
votes
Is quantum complexity basis-invariant?
This is a partial answer addressing only what I know: Stoquastic Hamiltonians in the Monte Carlo sign problem. The TLDR is, yes, complexity may depend on the choice of basis.
A stoquastic Hamiltonian ...
- 959
6
votes
Accepted
What is an example of an entangled state whose correlations are describable with a local hidden variable model?
It's easy to generate such a model for specific cases. For example, take the maximally entangled state $|\phi^+\rangle = \frac1{\sqrt2} (|00\rangle + |11\rangle)$, and let the observables in the CHSH ...
- 2,893
5
votes
Accepted
Are inseparable states with positive partial transpose nonlocal?
This question was solved in 2014 by Vértesi and Brunner: they found a quantum state with positive partial transposition that violated a Bell inequality. The conjecture that all states with positive ...
- 2,893
5
votes
Accepted
Definition of locality in Bell experiments
I think that I can explain the definition through the following simple example:
Suppose that you perform two experiments in the same house in two separate rooms. In the first you measure the ...
- 2,585
5
votes
Accepted
Shared entanglement to copy orthogonal states
Assume this works. Then, nothing prevents Alice from applying the same protocol to a quantum state that is known to her, such as $|0\rangle$ or $|1\rangle$. This way, she could send information to Bob ...
- 7,673
5
votes
Accepted
Difference between Bell's inequality and CHSH
The difference is as follows:
the original Bell inequality requires that outcomes from the same setting are always perfectly anti-correlated. It says nothing about the case where they are even ...
- 60.7k
5
votes
Accepted
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
\begin{equation}
\left|\int d\lambda p(\...
- 2,893
5
votes
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 ...
- 6,226
5
votes
Accepted
Why are only projective measurements considered in nonlocal games to get optimal strategy?
As you correctly state, POVMs can be dilated into a projective measurement on a larger Hilbert space. Because we do not restrict the possible dimension of the Hilbert spaces in the game, we can ...
- 6,226
4
votes
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 ...
- 60.7k
4
votes
Accepted
EPR states with permuted qubits
Let $S_x$ be a permutation between qubits 2,4 and 6, and acts as identity on the other qubits. Use $x$ to index all possible permutations of that form, of which there are 6. Then you do indeed have a ...
- 60.7k
4
votes
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 ...
- 60.7k
4
votes
Has anyone analyzed multi-round nonlocal games?
It seems that using more rounds will not be such helpful for us to get something more powerful from complexity perspectives. There are a few comments about the number of rounds and the number of ...
- 498
4
votes
Is quantum complexity basis-invariant?
I give this second answer to address a misconception that might be lurking in the question and to look at the local Hamiltonian problem: I am not entirely convinced by my answer and happy to hear what ...
- 959
4
votes
Accepted
Is quantum complexity basis-invariant?
The computational basis is "natural" in the sense that it provides a practical representation of measurement outcomes. Other bases are also "natural" for other tasks, and bases cannot be interchanged ...
- 3,432
4
votes
Accepted
Understanding Hardy's proof of "nonlocality without inequalities"
Answering your precise question: mixing the four scenarios is not particular to Hardy's argument, it is done in all nonlocality proofs. The fundamental assumption is that the distribution of the ...
- 2,893
4
votes
What is the difference between no signaling and non locality at operational and ontological level?
No signaling means can't be used for communication. Can't be used to move messages from a sender to a receiver.
Local means doesn't require communication to implement.
Some processes, such as ...
- 40.8k
4
votes
Accepted
What is the difference between no signaling and non locality at operational and ontological level?
I think the best way to understand this is by showing that one can violate (ontological) locality while respecting (operational) no-signalling.
Take the case of Bohmian mechanics. In it the result of ...
- 2,893
4
votes
Accepted
Role of convexity in proof of Monogamy of Bell correlations
This simultaneous block diagonalization is known as Jordan's lemma (not the complex analysis one though). It's a very common technique in the analysis of device-independent protocols as it allows you (...
- 6,226
4
votes
Accepted
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 ...
- 40.8k
4
votes
Is quantum computation effectiveness dependent on EPR non-locality?
No, because there's no need for the hidden-variable theory to be easy to simulate. It doesn't help at all to have everything pre-determined if it's computationally expensive to follow the evolution. A ...
- 2,893
3
votes
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 ...
- 2,893
3
votes
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 ...
- 60.7k
3
votes
Accepted
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 ...
- 40.8k
3
votes
Accepted
Understanding the idea of "local hidden state model"
It is equivalent to saying that Alice and Bob share a state of the form
$$\rho^{AB} = \int \mathrm{d}\lambda \mu(\lambda) |\lambda\rangle\langle \lambda| \otimes \rho_\lambda, $$
without any ...
- 2,893
Only top scored, non community-wiki answers of a minimum length are eligible