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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Kronecker product in the proof of Bell's inequality [closed]

In this answer it is said: You can easily verify, that $${\bf{\sigma}\cdot\bf{a} }|\psi^+\rangle=-a_x|\phi^-\rangle+ia_y|\phi^+\rangle+a_z|\psi^+\rangle$$ As usual, I need long effort to understand ...
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In Bell's inequality, why is the expected correlation given by $C_q(\mathbf a,\mathbf b)=-\mathbf a\cdot\mathbf b$? [duplicate]

In its article about Bell's theorem, wikipedia states here that the value of the correlation: $$ C_q(a, b) = \left\langle A \left|(\boldsymbol\sigma \cdot \mathbf b)^{(2)}(\boldsymbol\sigma \cdot \...
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Why is the assumption of free will important to physics [closed]

I have watched a few lectures and have heard in quite some places that free will is an important assumption in physics. For example Bell's theorem assumes that the two experimenters can freely choose ...
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Any experiment showing the “communication” between entangled particles is superluminal but not simultaneous OR simultaneous?

Do the numerous experiments that demonstrate a violation of Bell’s inequality also provide any data that the “communication” (I’m using that word for simplicity) between the entangled particles is ...
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Why does the correlation depend linearly on the angle, in the classical case of Bell experiments?

I am struggling to understand why we would predict the decay in correlation between the two measurements in a Bell Inequality experiment to be linear (see red line in this image from Wikipedia). I ...
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How Do I Calculate the Score of a Bell's Game

I am reading "Quantum Chance" by Nicolas Gisin. I would like to know how to calculate the Bell Game outcome given in the following section of the book. BACKGROUND The Bell Game begins with a pair ...
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What is an example of a steerable state that does not violate a Bell's inequality?

I understand that if a state violates Bell's inequality, it must be steerable. The relationship goes like this: $$\text{violates Bell's inequality} \Longrightarrow \text{steerable} \Longrightarrow \...
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Why quantum mechanics doesn’t break locality in entanglement but hidden variables theories will?

What makes it so that quantum mechanics doesn’t break locality in entanglement yet hidden variable theories will? In Bell‘s inequality said that hidden variables theories need to break locality in ...
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Components of Stern-Gerlach Filter

Came across a discussion of the EPR paradox and Bell's inequality in a psychology text. I started looking deeper into the Stern-Gerlach type experiments employed in the EPR discussion and found this ...
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I'm missing something basic in understanding Bell's theorem

I've read the wikipedia article, but I'm lacking some very basic understanding of entanglement probably. If I understand correctly, the experiment that is repeated is not time dependent, right? e....
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Help understanding prof. Steve Gull's explanation of Bell's theorem

Background Stephen Gull wrote this in his webpage "Many years ago (about 1984), I used to give a Mathematical Physics course to the Part II students. I illustrated the quantum paradox covered ...
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Concrete Example of Quantum Entanglement, Quantum Steering and Bell Nonlocality

I was reading the wikipedia page for quantum steering. The following is the mathematical way they have described the three notions: Is there any concrete example of these three concepts? Like, any ...
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Did the original EPR really consider an entangled state?

Or did only the subsequent thought experiments (Bohm & Aharonov, Bell) that introduced spin examine entangled states? The wikipedia article titled 'EPR paradox' claims as much: 'The thought ...
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Why would the classical (local) correlation in Bell's experiment rule out the cosine of the angle?

This question expands on a specific detail of this previous question: Why would classical correlation in Bell's experiment be a linear function of angle? I would have commented on/answered that ...
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What's quantum about quantum discord?

Quantum discord is a quantity that relates two subsystems of a quantum state. It reduces to the entanglement entropy for pure states, but it differs for mixed states; separable states have zero ...
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In Bell's inequalities, how is realism violated, and how can one preserve locality?

I have heard the violation of Bell's inequalities asserts either realism or locality needs to be abandoned. I understand the notion of locality being violated but can someone explain how realism is ...
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Is there a class of Bell inequalities that are violated by certain mixtures of known orthogonal entangled states?

Is there a class of Bell inequalities that are violated by certain mixtures of known orthogonal entangled states? There exist a multitude of classes of Bell inequalities that can be used in ...
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Do distillable states necessarily violate the CHSH inequality?

Let $\rho$ be a bipartite quantum state. If $\rho$ is distillable will it necessarily violate the CHSH inequality ($|\langle A_0(B_0+B_1)+A_1(B_0-B_1)\rangle| \leq 2$)?
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Do Feynman path integrals satisfy Bell locality assumption?

There are generally two basic ways to solve physics models: Directional, e.g. Euler-Lagrange equation in CM, Schrödinger equation in QM. We evolve some initial conditions in some direction, can ...
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Implications of MIP*=RE for physics?

Background Earlier this month (Jan 2020) a pre-print was posted to the arXiv claiming to have proved the equivalence of the complexity classes $\mathrm{MIP}^{*}$ and $\mathrm{RE}$ (see below for ...
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Do humans entangle particles, or are they already entangled?

I recently visited our city hall and there was an exhibition which featured one of our local physicists, a John Stewart Bell. Although it was presented well the technical information was very basic. I ...
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Violation of Bell-like inequalities with spatial Boltzmann path ensemble: Ising model?

Quantum mechanics is equivalent with Feynman path ensemble, which after Wick rotation becomes Boltzmann path ensemble, which can be normalized into stochastic process as maximal entropy random walk (...
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Has anyone combined measurements of the Bell inequality with special relativity?

The Bell inequality as measured with polarization involved slits polarized in either the same or a different orientation with respect to the photon emitter. If I understand and/or recall correctly, ...
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Is this interpretation of Bell's theorem correct?

A popular interpretation of the Bell's theorem is like this: Take a set of objects with three boolean properties, say, $x$, $y$, and $z$. For each object, randomly pick two of the three properties ...
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CHSH inequality vs. Tsirelson's inequality

CHSH inequality says that given four classical observables $a$, $a’$, $b$ and $b’$, the observable $$C= ab + a’b +ab’ - a’b’$$ satisfies at most $$| \langle C \rangle | = 2$$ if we choose the “...
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Proof of $P(\mathbf a,\mathbf b)=-\mathbf a\cdot\mathbf b$ in Bell’s original paper

Bell’s original 1964 argument works by comparing a QM prediction with the prediction of a local hidden variable theory. In the notation of Griffith’s version of it in ”Introduction to Quantum ...
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Is the Bell's paper on the EPR paradox coherent?

I tried to read the Bell's paper on the EPR paradox but i rapidly stepped on difficulties : $$A(\vec{a}, \lambda) = \pm 1 ,\ B(\vec{b}, \lambda) = \pm 1 \tag{1}$$ So we identify $A$ with particle 1 ...
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Shouldn't classical physics force us to assume that there is determinism on a quantum scale?

I'm not a physicist, I have read a lot about Bell's theorem and the Einstein/Bohr debates and I have the following question: Judging by only classical physics, it seems we live in a 100% ...
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Which spin-1/2 photon states can be used in the context of Bell's inequality violations?

In textbooks, the violation of Bell's inequality is usually demonstrated for spin-1/2 systems in the state $$| \psi \rangle = \frac{1}{\sqrt{2}} \left( | +- \rangle - | -+ \rangle \right).$$ Most ...
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Why are both of these forms of the CHSH inequality correct?

Most of the time, when looking up the CHSH inequality, I find something like $$E(0,0)+E(0,1)+E(1,0)-E(1,1)\leq 2.$$ But other times I find something along the lines of $$\vert E(0,0)+E(0,1)\vert+\...
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Is it possible to actually run Sidney Coleman's “Diehard” experiment?

I just rewatched Sidney Coleman’s famous lecture “Quantum Mechanics, In Your Face”. I say “rewatched” because I had the privilege to attend his repeat of this lecture at UCSD in ’94 or so. But ...
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John Bell's formulation of the Bell Inequality [closed]

In "ON THE EINSTEIN-PODOLSKI-ROSEN PARADOX" by Bell(1964), Eq(14) says: $$ \begin{align} P(\vec{a},\vec{b}) &=\int{d\lambda\rho(\lambda)A(\vec{a},\lambda)B(\vec{b},\lambda)}\\ &=-\int{d\lambda\...
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Can unitary probability theory (quantum mechanics) emerge from a lack of information about a deterministic process? [duplicate]

My initial question below appears to be unclear so I am rewording in more succinctly here. The pre-edit question remains below. There exists two types of probability theory: 1-norm (classic ...
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The Function of the Free Will Assumption in No-Go Theorems [closed]

I'm interested in the function played by the free will assumption made by any number of no-go theorems in quantum mechanics. While searching the archives for prior questions, I found this one from 5 ...
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Can massless particles change their quantum state? What about with entanglement?

It is well established that any massless particle, by special relativity, must travel at the speed of light, e.g. Special relativity and massless particles. Accordingly, this means that massless ...
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Could the definition of the experiment result occur before measurement?

Is there any fundamental demonstration that result of an experiment cannot have been determined before the measurement, yet according to the probabilistic rules of quantum mechanics? I understand ...
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What is the local, non-realist explanation of EPR correlations?

Bell's theorem proves that local hidden variables theories cannot reproduce quantum mechanics (with the exception of superdeterministic theories). Are there any local theories that do not involve ...
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What is the physical basis behind the independence assumption in Bell's theorem?

Bell's theorem rests on two main assumptions: locality and independence. Locality has its basis in relativity and it seem to be a property of all known physical theories accepted today (General ...
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Understanding Bell's inequality

I'm struggling to understand Mermin's article "Is the moon there when nobody looks?". In this article, a Bell experiment with three measurement settings is discussed. Is it possible to reduce the ...
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Do Bell’s inequalities assume particles can only have one variable to consider?

I have asked the question “How do you know when pairs are entangled?” I have asked “What is the difference between entangled and correlated?” I have also asked several similar questions, but I keep ...
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Why does the effect of measuring an entangled particle is not apparent when examining only one particle? [closed]

As far as I understand, the Bell test experiments show that observations (measurements) of entangled particles have an effect on one another. This effect is apparent when examining the results of ...
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Can Quantum Entangled particles convey information faster than speed of light? [duplicate]

Can Quantum Entangled particles convey information faster than speed of light. If they don't what was wrong with John Bells experiment?
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Is the Proof of Gisin's Theorem Wrong?

I have been trying to understand Gisin's paper, Bell's inequality holds for all non-product states. As I've worked through the proof he provides for his theorem, I've run into two things that simply ...
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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 ...
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Is there a systematic method to derive Bell's inequalities?

BACKGROUND The purpose of Bell's inequalities is to put bounds on certain combinations of classical measurement probabilities. One can then show that quantum entanglement can yield probabilities that ...
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Can we exlain Bell's Theorem without dwelving into Quantum Mechanics?

I have recently started learning Quantum Mechanics. We learnt some things on light polarization, so I referred to this site. Luckily I stumbled upon this answer which links to this site which sated my ...
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Does reality express non-local realism, local non-realism or non-local non-realism? [closed]

So I read that Bell's tests prove that reality cannot follow the requirements of both realism and locality. My understanding is that: Realism: Objects have definite properties before they are ...
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How are contextuality and locality related?

I know how quantum non-locality is defined in Wikipedia quantum nonlocality is a characteristic of some measurements made at a microscopic level that contradict the assumptions of local realism ...
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Prove that in Bell's inequality $\langle{\Psi}|\left(\bf{\sigma}\cdot\bf{a}\right)\left(\bf{\sigma}\cdot\bf{b}\right)|{\Psi}\rangle=-\bf a \cdot\bf b$

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\...
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Can quantum randomness be somehow explained by classical uncertainty? [closed]

In quantum mechanics, the outcome of each measurement is random, distributed according to the squared amplitude of the wave function obtained from the Schrodinger's equation. Now, can someone suggest ...

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