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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.

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How to calculate guessing probability for quantum key distribution?

There are 3 Projections $P_1$, $P_2$, and $P_3$ corresponding to 3 inputs $x = 1, 2, 3$ for Alice. Similarly, the same projections are used by Bob for $y = 1, 2, 3$. Each input has 2 outcomes, $a = 1, ...
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State after measurement in "Delayed choice for entanglement swapping"

I'm reading this paper below, but it seems to me the conclusions are not correct. https://arxiv.org/abs/quant-ph/9904042 Alice and Bob independently prepare the Bell state $\Psi^-$. They measure one ...
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Bohmian mechanics, Leggett inequality, realism and nonlocality

Very often it is said that the Bell inequality has ruled out the possibility of hidden variables (HV) in QM. This is incorrect since Bell inequality has ruled out local hidden variables: nonlocal HV ...
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Defining the geometry of Bell inequalities

Bell inequalities can be discussed in the language of geometry. In papers such as [1], there is a general flow of definitions leading to the geometric picture of Bell inequalities: $$\text{Behaviors} \...
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Entangled Photons passing different polarizers

Consider two entangled photons leaving a source. Both are polarized at angle 0. One travels to the left and the other to the right. The one on the left encounters a polarizer at 30 degrees and the one ...
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Are states partially ordered in the same way via entanglement and Bell violations?

Recall what a partially ordered set is. Let $E(\rho)$ be an entanglement measure. Let $B(\rho) \leq 0$ be a Bell inequality. Define the Bell violation measure with respect to $B$ as $$\tilde{B}(\rho) =...
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Why can we not experimentally evaluate the expectation value of the CHSH operator after simplifying its expression to check entanglement?

We have the observable corresponding to the CHSH inequality given by, \begin{align} \mathcal{\hat{S}} &= \hat{Z}_1 \left(\frac{1}{\sqrt{2}} (-\hat{Z}_2 - \hat{X}_2)\right) + \hat{X}_1 \left(\frac{...
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False-positives in Bell-like Inequality Violation (CHSH specifically)

Previously I asked how it makes sense for dark-counts/inefficiencies to affect loop-holes in Bell's Inequality: I have a different question: What are all the possible false-positives in a Bell-like ...
Steven Sagona's user avatar
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Why does detector inefficiency (or dark counts) count as a "loop-hole" in Bell-inequality tests?

Conceptually, I don't see why there is a problem with nonunity dection inefficiency or dark counts in a bell-inequality-measuring experiment. Intuitively, isn't the point of the Bell-inequality to ...
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Bell's inequality in Claude Cohen-Tannoudji's Quantum Mechanics Volume III

Claude Cohen-Tannoudji et al, Quantum Mechanics Volume III, 2020 edition, Chapter XXI.F-3-b.$\alpha$ (F-7) on p.2210 states $$\big\langle\hat A(a)\hat B(b) \big\rangle={\cal P_{++}+P_{--}-P_{+-}-P_{-+}...
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Why does the quantum expectation in Bell's inequality have to take on the form of a quantum probability measure in Valter Moretti's book?

Valter Moretti, Fundamental Mathematical Structures of Quantum Theory Section 5.3.1 on Bell's inequality on p.204 as shown below states in Equation (5.8) that we have to interpret the expectation $E_\...
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Why are wavefunctions not considered hidden variables?

In the proof of Bell's theorem of 1964, referenced e.g. here, the definition of a hidden variable seems to be any variable from which we can derive the correlation between the detectors, by ...
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Why a probability distribution in RHS in deriving Bell's Inequality?

Why is there typically an integral over a probability distribution in the RHS of a derivation of Bell's inequality $$|P(\boldsymbol{a}, \boldsymbol{b}) - P(\boldsymbol{a}, \boldsymbol{c})| \leq \int{p(...
No infinity's user avatar
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All the logically possible ways to get around Bell-type inequalities

I'm a high school student, so my (mis)understanding here is not very rigorous or precise, but I will write it below so as to concretely frame my question: Bell's theorem takes three assumptions ...
user110391's user avatar
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Does Bell’s theorem rule out changing hidden variables?

In the EPR experiment, it is said that there are predictions that are made if there are hidden variables determined by something locally in each particle that results in a correlation in entanglement. ...
Alejandro's user avatar
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Do Bell’s inequalities assume determinism?

I was watching a video of Tim Maudlin where he talks about how the CHSH version of Bell’s inequalities do not assume determinism and only assume locality. He said that it is a common misconception ...
inquisitive 's user avatar
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How do we know that the double slit experiment can’t be explained by a deterministic theory?

Bell’s inequality applies only to very specific kinds of systems where there is entanglement and non local correlations. Those phenomenons are by every account special. As far as I know, there is no ...
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How do we arrive at the Bell polytope constructed starting from definition of behaviours?

While reading Valerio Scarani's book ; Bell Nonlocality I came across section 2.4 where the author tries to represent the set $\mathcal{L}$, of all local behaviours as a polytope. The term behavior ...
Uranium238's user avatar
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Does rotation the polarization of one twin photon rotate the other?

After a nonlinear crystal there are two photons in HH+VV state. What happens to the state if one of the photons in the pair is rotated? Does the state stay the same or it flips to HV+VH?
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Does local realism imply entangled photons are equal (or opposite)?

I'm watching a video about Bell's inequality and how there can be no local hidden variables. They explain it using photons and whether they pass through a polarizer or not when they're oriented at ...
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How can resolution of particle entanglement be detected, and why can't it be faster than light communication?

Sorry for the length, but this is driving me crazy. And yes, there are other questions on this issue and I have reviewed them, but I cannot see the answer stated simply. What is different about my ...
RalphBerger's user avatar
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Understanding operator product of three mixed states with three projector operators

I am recently studying the triangle scenario in the context of Bell nonlocality (for reference, see for instance this article). In it, we have three parties, commonly referred to as Alice, Bob and ...
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Bell inequalities after twin paradox?

Imagine the usual twin paradox, a twin stays on Earth, the other twin leaves in a rocket reaches $c(1-\epsilon)$ speed for small $\epsilon$ and the twin turns around and goes back to Earth at the same ...
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What interpretations are ruled out by the Kochen–Specker theorem?

What interpretations are ruled out by this theorem (such as superdeterminism, Bohmian mechanics, or ensemble interpretations) and does it function similarly to Bell's theorem as a 'no-go' theorem?
Marco Fabbri's user avatar
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Can Leggett-Garg inequality be used to falsify realist interpretations of quantum mechanics?

Can Leggett-Garg inequality be used to falsify superdeterminism, Bohmian mechanics and other realist interpretations of quantum mechanics? https://en.wikipedia.org/wiki/Leggett_inequality https://en....
Marco Fabbri's user avatar
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3 answers
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Do properties of quantum particles 'exist' before observation? [closed]

We understand that quantum particles have properties like 'spin'. And upon observation, the value of this property is determined. Before observation, the value is non-determined and the wave function ...
ImTalkingCode's user avatar
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Why is $\lambda$-sufficiency necessary for No-Go Theorems?

In a talk given by Spekkens (Why I Am Not a Psi-ontologist) at 4:00 he talks about an assumption called $\lambda$-sufficiency which is part of any no-go theorem of quantum mechanics. It is described ...
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Confusion around Bell's Theorem and Locality

I recently got interested in foundational aspects of quantum mechanics and I have some questions: Bell's theorem proves that any local, deterministic theory with statistical independence can't account ...
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Spin Correlation Analogy in Three Particle System

I have recently gone through the section on Bell's Inequality in "Modern Quantum Mechanics" by J.J. Sakurai and Jim Napolitano and I am curious as to weather or not there are analogous ...
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What do we mean by causality when we say that entanglement measurements are uncaused? [duplicate]

I’m having a hard time wrapping my head around how the measurement of particle A does not affect the state of an entangled particle B even if no superluminal speeds exist. Suppose Alice makes a ...
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Equivalence between CGLMP inequality and CHSH inequality

In this paper, they claim that the inequality $$I = P(A_1 = B_1) + P(B_1 = A_2 + 1) + P(A_2 = B_2) + P(B_2 = A_1) \leq 3$$ is equivalent to the CHSH inequality $$|E(A_1,B_1) - E(A_2,B_1) + E(A_2,B_2) +...
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Can there be a local hidden variable theory that works differently for each electron in an entangled pair?

I recently watched a video from Brian Greene that goes over an example of Bell’s inequality. Video here. In this example, he imagines the generation of a pair of entangled particles, each of which is ...
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1 answer
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Partial Measurement of a Bell State: How to project a Bell state onto its new "eigenbasis"?

In Alain Aspect's talk "Bell’s Theorem: The Naive View of an Experimentalist", Aspect explains the strong correlations in an EPR experiment where both polarisers are in the same orientation. ...
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Does a process that creates a pair of photons have the same polarization and also the same output of a hidden variable if it existed?

After watching this video on Bell’s inequality here, it mentions that if you have a process for pair production, in this case a photon pair where the photons travel in opposite directions, the ...
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6 votes
3 answers
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Bell's inequality for angles 120°

In 1964, John Bell first derived the original Bell inequality, $|E(a,b)-E(a,c)|\leq1+E(b,c)$. Here $a,b,c$ are three different possible spin measurement directions, and $E$ is the measured ...
Subhajit Podder's user avatar
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Is there any notion of device independent test for correlation like quantum discord?

A Device independent test is a procedure used to characterise quantum resources with the minimal level of trust. If one wants to test correlations like entanglement in a device-independent way, we get ...
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How we know that spin of two entangled photons are not predifined? [duplicate]

If we take two balls that change colours white and black, if we set that change in colours is always opposite one from another, for sure if we take one ball to the end of universe, if that ball will ...
user78495162's user avatar
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1 answer
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In what sense is Bell's inequality "probabilistic", while the GHZ experiment is "definite"?

I read the paper about the GHZ contradiction written by David Mermin and he said that Bell's inequality is probabilistic while GHZ experiment is definite. Here is that paper:https://journals.aps.org/...
Alex's user avatar
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How do proponents of superdeterminism explain the specific choice of values for the hidden variables that violates the Bell inequality?

I don't have a background in physics, but I have an amateur interest in quantum mechanics, and I recently found out about the notion of superdeterminism. From what I understand, superdeterminism ...
BackusNaur's user avatar
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Can a point in the quantum set of correlations violate more than one independent facet Bell inequality?

Usually, depictions of the quantum set of correlations and the local polytope look something like: In this image it looks like non-local points belonging to the quantum set (in yellow) violate only ...
neilps2000's user avatar
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Is there any minimalistic version of superdeterminism theory?

Superdeterminism is one wild conjecture which is an alternative to the standard quantum mechanical interpretation and preserves local realism Superdeterminism seems to be too much of a stretch. If ...
Hari Kumar's user avatar
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2 answers
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Is spooky action at a distance real or does hidden variables exist? What does it mean in context of free will? [closed]

I am complete amateur at this and research about physics is just a hobby for me. So with that in mind here is my problem: I saw a few debates between physicists about spooky action at a distance vs ...
comp_guy_dude's user avatar
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Experimental Demonstration of Entanglement?

In many papers about entangled sources, they use an experimental setup like this one to demonstrate their entanglement: The setup involves measuring coincidences at the detectors at various angles of ...
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2 answers
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Is the possible Bell's test loophole of entangled particles communicating at a non instantaneous but FTL speed addressed and eliminated? [closed]

TLDR: There seems to be a loophole in Bell's test that is not addressed or eliminated before we can successfully conclude that it proves that the Universe is unreal and non local. The entangled ...
Hari Kumar's user avatar
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1 answer
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Deriving probability in Bell's inequality

Measuring the spin with an arbitrary angle $\theta$ with respect to the plane xz we obtain the spin operator (multiplying Pauli matrices per the projection $(\cos\theta,\sin\theta)$) $$\hat{\mathrm{S}}...
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How can we be sure Bell's theorem disproves local realism when we are not sure whether the measuring apparatus is in some form of entanglement or not? [duplicate]

Bell's therorem seems to disprove localism because measuring, let's say spin of an entangled electron, seem to communicate the measurement to it's another pair instantaneously. But isn't another thing ...
Hari Kumar's user avatar
1 vote
1 answer
77 views

Can you provide an example quantum system that violates Bell's inequality? [closed]

I am self-learning QM. I am reading this paper about Bell's theorem https://arxiv.org/pdf/1212.5214.pdf and having difficult to understand the quantum system example in the paper that violates Bell's ...
Yang Wang's user avatar
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Why does it make sense to add/subtract the results of measuring in 2 different bases in Bell's inequality when each observer only measures 1 property?

In the CHSH inequality, we construct an experiment whereby two observers each receive a particle and measure two given properties of their particles, for which the outcomes are ±1. We then consider ...
David's user avatar
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Entanglement correlations 2 [duplicate]

About the alleged duplicates: " Quantum entanglement vs classical analogy" "Show quantum entanglement to a classical thinker" refer to black and white balls that would have a ...
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Understanding superdeterminism

I was reading about superdeterminism and it was a bit counter-intuitive. The idea of having a hidden variable on the measurement device is very rational. For example, if we emit light to a constrained ...
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