Questions tagged [bells-inequality]

Bell's inequality is a no-go theorem contrasting crucial correlations of physical observables in QM to those of the world as described by classical mechanics, essentially local hidden variables theories serving as a viable "explanation" of QM: QM inevitably violates these inequalities, as observed. Further use for the CHSH inequality generalization.

0
votes
3answers
281 views

Shouldn't local realism imply the superdeterminism?

I see that Bell has ruled out Einstein's local realism but not supredeterminism. I see that Bell has confessed that superdeterminism kills his inequality. You cannot apply Bell's inequality if ...
8
votes
2answers
783 views

Tracking down the locality assumption in a CHSH inequality derivation

CHSH inequality requires both locality and realism. I will equate here realism with counterfactual definiteness. Now counterfactual definiteness tells us that given two different measurements on the ...
-1
votes
2answers
174 views

Would Einstein have accepted the presumptions that lead to the Bell inequality?

To check the correlation between Hidden Variable Theory and Quantum Mechanics, Bell calculated the expectation value $$<\sigma_{e}(\vec a,\vec V) \sigma_{p}(\vec b,\vec V)> = \int d^n V \rho(\...
1
vote
1answer
137 views

Does Bell's theorem imply nonlocality using a false assumption?

In https://arxiv.org/abs/1409.5158, the author concludes that Bell tests cannot refute local realism, because they employ a wrong analysis. He says: "The quantum joint prediction cannot be ...
1
vote
1answer
30 views

Is the electric charge associate with quantum systems counterfactual definite?

Is the electric charge associated with quantum systems counterfactual definite? Counterfactual definiteness refers to the inability to ''speak'' meaningfully (in quantum systems) of the definiteness ...
1
vote
1answer
45 views

Dimension of joint probability space in the Bell Scenario

In the Bell(CHSH) scenario with the normal two qubits+two measurement settings, how does the dimension of the joint probability space $ P(ab|xy)$ drops from 16 to 8? In general, for two d-dimensional ...
1
vote
1answer
80 views

How to quantify the level of non determinism / randomness in the universe

I recently read a little about the Bell test (I'm not a physicist, but reasonably well educated) and I started wondering if there is a way to express the level of non-determinism as a single number ...
1
vote
1answer
52 views

Restrictions on Bell-type inequalities

While deriving and proving Bell-type inequalities of the form $|E(a,b)-E(a,b')|+|E(a',b)+E(a',b')|\leq 2$ I know that the conditions on the operators $O_a$ and $O_b$ are that they must be bounded ...
0
votes
1answer
83 views

Bell inequality proof

I am trying to understand how the correlation function in John Bell's paper on EPR is derived for a spin singlet state $|{\Psi}\rangle$. This is defined to be $$ \langle{\Psi}|\left(\bf{\sigma}\cdot\...
0
votes
1answer
83 views

Wigner Function for an Entangled Composite System

How is it possible to compute the Wigner function for a composite system that is prepared in an entangled state? In particular, consider the state $|ψ_{AB}\rangle=\frac{1}{\sqrt{2}}(|0_A\rangle|1_B\...
0
votes
1answer
90 views

Is linear polarization of entangle photons in 2-particle decay always correlated?

In Aspect's paper "Bell's Theorem: The naive..." and in an 2002 AJP article by Dehlinger and Mitchell "Entangled photon apparatus..." the photons are described to be in the $|xx\rangle+|yy\rangle$ ...
-1
votes
1answer
162 views

Entanglement = Steering = Non-Locality?

For a simple case of two party system. What I understand by Entanglement(please correct me if I am wrong) is that if some property of the two systems is entangled, then knowing one, provides the ...
27
votes
0answers
602 views

Bell polytopes with nontrivial symmetries

Take $N$ parties, each of which receives an input $s_i \in {1, \dots, m_i}$ and produces an output $r_i \in {1, \dots, v_i}$, possibly in a nondeterministic manner. We are interested in joint ...
5
votes
0answers
106 views

Is Quantum Correlation A Correlation in Statistics?

One can read in Wikipedia that quantum correlations are the expectation value of the product of the outcomes on the two sides which indicates that $QC(a,b)=\langle( \vec\sigma \cdot \vec a)^{(1)}(\...
2
votes
0answers
279 views

If correct, Bell's Theorem rules out local variables and suggests a superdeterministic for to the Universe?

If Bell's Theorem is correct and Quantum Mechanics cannot rely upon 'local variables'. Bell suggests that a probable solution is the existence of a Super-determined order upon the construct of our ...
2
votes
0answers
156 views

Is Bohmian mechanics incompatible with Leggett inequality?

As far as I know violation of Bell's theorem is not a problem for De Broglie–Bohm theory because this theory is explicitly nonlocal; But since the violation of Leggett inequality is considered to ...
2
votes
0answers
118 views

Confusion by Murray Gell Mann video and Bell's Theorem

I'm trying to understand 3:02 in this video: https://www.youtube.com/watch?v=AlIlkn3OxMI&t=184s He seems to be saying that the measurement of a property one photon has no effect on the other. So ...
2
votes
0answers
24 views

Does the trial index of typical CHSH experiments constitute a “hidden variable”?

In typical experiments related to the CHSH inequality there are individual detections being made by two separate (analyzer-and-)detector systems, "System $A$: $(D_A^+, D_A^-)$" and "System $B$: $(D_B^+...
2
votes
0answers
102 views

Is there a cheap way I can do a Bell inequality experiment?

My work is almost completely theoretical/computational. But I'd really like to do a Bell inequality experiment just so I can personally see this (the best way to learn something is hands-on, right?) ...
1
vote
0answers
41 views

How is Mermin's magic square computed?

BACKGROUND The Peres-Mermin magic square consists of different combinations of tensor products of Pauli operators being applied on an arbitrary bipartite state. Suppose we're considering the entry in ...
1
vote
0answers
52 views

What is the variance of |S| in Bell's inequality (CHSH inequality)

Sorry that this isn't a quick question but I didn't know how to make it shorter. I am struggling with this for quite a long time and I would appreciate every help that I can get. I could not find a ...
1
vote
0answers
162 views

Local determinism vs. Local realism vs. Local causality

I found the following definitions for the three different terms. Do you find these definitions exhaustive, or can you suggest more precise formulations? Quoting the wikipedia page on Local realism: ...
1
vote
0answers
49 views

Can local hidden variables models be ruled out without invoking expectation values?

Bell's inequalities, in their standard form, are a statement about the limitations faced by a probability distribution that can be written as $$p(a,b|x,y)=\sum_\lambda p(\lambda) p(a,b|x,y,\lambda)=\...
1
vote
0answers
35 views

Are there Bell test experiments that don't require coincidence monitor?

CHSH (2-channel) for instance doesn't count for a case where all 4 channels didn't detect anything (simultaneously) at some point in time. As I understand, such all-absence shouldn't happen/matter at ...
1
vote
0answers
106 views

Relativity and Bell's inequalities

I am reading a collection of interviews taken with prominent physicists as in an aftermath of famous Alain Aspect experiment. Between them John Bell states that if local realism has to go, he would be ...
1
vote
0answers
88 views

Is there any basis in stating there are different levels of 'locality' or 'reality', within physics or physical theories?

EPR’s reality criterion and quantum realism has this paragraph (the paper has 0 citations, and I'm personally happy to call this metaphysics, but still!): A popular interpretation of Bell’s theorem ...
1
vote
0answers
62 views

What's a comprehensive review of the implications of Bell-nonlocality on our notion of reality / Weltanschauung?

I am looking for a (preferably peer-reviewed) article that summarizes: the historic debates surrounding Bell-nonlocality, how nonlocality can/not be reconciled with our notation of reality, and ...
1
vote
0answers
51 views

Understanding the classical expectation side of EPR/Bell inequalities

I like building educational models[1], and I’m collecting ideas for a quantum physics based one. I’m wanting to make sure I’ve got my head around the classical side of the Bell inequalities, ...
1
vote
0answers
75 views

Bell's inequalities and distributive logic

I saw somewhere that the famous Bell's inequalities in quantum theory are related to the distributive law in the classical set theory. Is this true? More precisely, the inequalities are consequences ...
1
vote
0answers
72 views

Non-linear bell's inequality?

Consider the Bell setting, where Alice and Bob get inputs $x,y$ and they perform measurements $\{M^x_a\}_a,\{N^y_b\}_b$ respectively on their shared pure state $\Psi_{AB}$ to obtain outputs $a,b$. ...
1
vote
0answers
31 views

Does it make sense to add overlapping probabilities > 1?

I read about a variation of Bell's inequality, expressed as $$P_\text{same}(A, B) + P_\text{same}(A, C) + P_\text{same}(B, C) ≥ 1$$ It is later shown that the inequality is violated using QM. ...
1
vote
0answers
187 views

Bell's inequality

For a project, I'm planning to study Bell's inequality, which as far as I can gather is taken to rule out hidden variable theories of QM. I'm looking for recommendations of decent sources which derive ...
1
vote
0answers
71 views

What characterizations are available for two-photon Bell state light sources?

It is often technologically important to know how photon statistics change over time when a light source is turned on. A light source that comes to full intensity/visibility in a nanosecond after it ...
0
votes
0answers
19 views

How would a “loop-hole free” Bell test appear to an observer moving at relativistic speeds compared to Alice and Bob?

How would a “loop-hole free” Bell test appear to an observer moving at relativistic speeds compared to Alice and Bob? In most such tests, Alice and Bob are 1km+ away from each other to prevent ...
0
votes
0answers
43 views

What's the invariance quantity under EPR and Bell's inequality?

I was reading and writing a study report about EPR and Bell's inequality. As the hidden variable and local realism was proven to be "false", and from many posts in physics exchange websites such as ...
0
votes
0answers
41 views

Probabilities of sequential measurments of spin 1/2 particle

I'm interested in checking why my working for the following problem does not agree with the expected result. In a section describing Bell's Inequality, the following sequence of measurments is ...
0
votes
0answers
34 views

I wasn't able to find a good resource for Bipartite state and Bell's theorem

Our professor used tensor product to explain bipartite operator and states and then he used the new operator and state to explain Bell theorem. I wasn't able to find a good resource or reference for ...