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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Looking for Experimental Result Data for Bell's Inequality, especially at 60 degrees

I've been looking for an experiment (for Bell's Inequality, using Bell's 60 degree test angle) which shows counts and resulting correlation percentage calculated. I want to see if a) for 99 runs 66 ...
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Inclusion-exclusion principle in modeling interactions

When I was in school, I couldn't accept the concept of binary pairwise additive interactions, aka "Force" in classical physics. For me, the emergence of magnetism was a clue that for a 3-...
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Specifications of Bell's inequality experiments conducted untill now

Has any Bell's inequality experiment, conducted until now, which has satisfied the following criteria? Having more than three measuring orientations. In the typical experimental setup I have seen ...
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What is local about the hidden variable in Bell's theorem?

A pion decays to a singlet electron/positron state. We will measure the component of the electron's spin in the $\vec a$ direction and positron's spin in the $\vec b$ direction. If there exists a ...
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How to test if a bipartite density matrix violates Bell's inequality?

For a given density matrix $$\rho = \sum_{ijkl=0}^1 r_{ijkl} |i,j\rangle \langle k,l|$$ describing a bipartite two-qubit system, how can I prove for what values $r_{ij}$ the density matrix violates ...
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On the Bell's Theorem / Bell-type Inequalities and the Kochen-Specker Theorem

It appears to me that the Kochen-Specker theorem, if not Gleason’s theorem already, seals the fate of realism / value definiteness (with possibly the additional assumption of non-contextuality, ...
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How can a basis change make a state suddenly separable?

I am working through my quantum optics textbook by Grynberg, Aspect and Fabre, and this concept has tripped me up a little. (13) is an inseparable state, whereas (15) IS separable - but they are the ...
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A notational confusion in a Bell-type inequality

In the tripartite Bell-type inequality know as Svetlichny inequality, given in this (freely available) article. The quantity $M_{ijk} = Tr [\rho(\sigma_i \otimes \sigma_j \otimes \sigma_k)]$, $i,j,k\...
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What happens to linear terms like $\langle \psi| \hat{a}\cdot \vec{\sigma} | \psi \rangle$ in CHSH inequality?

The CHSH inequality is given by (e.g., 4.33 here) $$\langle E_a E_b\rangle + \langle E_{a^\prime} E_b\rangle + \langle E_a E_{b^\prime}\rangle - \langle E_{a^\prime} E_{b^\prime}\rangle \le 2,$$ where ...
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With how much $\sigma$ was Quantum Mechanics (QM) proven over Local Hidden Variable Theories (LHV) in experiments?

My question is how "sure" experiments are that QM is the right theory over LHV. I heard that the last bell inequality experiment came to the conclusion that QM was right with a certainty of $...
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Uncertainty Principle Violations?

I’m learning about Bells Inequality Experiment and have a question because the instructor in the video I am watching simply passed over something I found jarring. Ok, you have your entangled pairs of ...
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What is required for a minimum viable Bell test experiment at home?

My objective is to create a tabletop Bell test experimental setup generating data of suitable quality for undergraduate education or satisfaction of personal curiosity; remaining free from loopholes ...
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How to derive the theorem about CHSH inequality in the $\mathbb{C}^2\otimes\mathbb{C}^2$ space in (Horodecki, 1995)?

In the $\mathbb{C}^2\otimes\mathbb{C}^2$ space, a state can be represented as: \begin{equation} \rho=\frac{1}{4}(\mathbb{I}\otimes\mathbb{I}+\mathbf{r}\cdot\mathbf{\sigma}\otimes\mathbb{I}+\mathbb{I}\...
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Availability of dataset from "Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres"?

I am looking for the most-raw data from the (in)famous Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres experiment. I would like to try repeating their ...
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Do all entangled states violate some Bell inequality?

Suppose I have a multipartite pure entangled two-level system. Is it always possible to form a bell-inequality based on this state such that the observed correlations cannot be reproduced classically? ...
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A popular explanation of Bell's inequalities

In one book on quantum mechanics, I found a very simple analogy to Bell's inequalities, which explains their essence without delving into the details of the physical experiment. I liked this analogy, ...
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In Bell's experiment, can "knowing the future" be that "hidden variable"?

(Sorry if I'm spamming your board with Popular Science speculations, but I just thought this could be an interesting thought experiment). There are quite a few videos on youtube about Bell's ...
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Measuring spin at an angle. Why is the probability $p = \cos^2(\theta/2)$?

In this video about quantum entanglement, at 1:38, it is said that "the probability [of spin being in the same direction with the measurement] depends on the square of the cosine of half the ...
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What's wrong with this extremely simple hidden variables approach?

I've seen the Veritassium video about Bell's theorem which made me think about what the hidden variables could be. I'd like somebody to explain to me what's wrong with this extremely simple hidden ...
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Diagonalization of an operator with two Hilbert's subspaces

I was thinking how to diagonalize an operator which is composed by two Hilbert's subspaces. For example, the Bell's operator, which is defined as \begin{equation} \vec{B} = \vec{\sigma_1}\cdot \vec{a}(...
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Is there a source for this equation for a Bell's Theorem test?

In this, he gives an example of entangled photons spin being measured – one photon sent to a detector at $0^\circ$, and the other photon sent to a detector at $20^\circ$. He says the odds of both ...
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Typo in Bell's original paper on the EPR paradox?

I am trying to understand Bell's famous paper from 1964 on the EPR paradox. I stumbled over equation $(9)$ where it says $$\left.\begin{align}A(\vec a,\vec\lambda)&=\operatorname{sign}\vec a\cdot\...
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Implications of Bell Violation in Classical Optics for Local Realism [closed]

A recent set of articles (one in Nature, a second in Entropy, a third in the Journal of Physics B) declared that BCHSH violations by themselves do not rule out the possibility of constructing local-...
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What is the difference between the EPR paradox and Bell's inequalities?

I am a newbie here, hope I will be able to get accustomed on this forum. I am trying to understand what quantum entanglement is. Obviously, for this it is very useful to understand Bell's theorem. ...
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Superdeterminism clarification?

I see superdeterminism come up as one way that local realism and all that other good stuff can be preserved, but it also seems like it's a minority view. I've been trying to understand why, and really,...
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Is there any relationship between the recent LHCb results on lepton universality violation and Bells Ineqalities? [closed]

Link to article re LHCb results As a layperson, my knowledge is limited to what i can understand from pop sci books. Having recently read about (although not quite understood!) Bells Theorem, it ...
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Has there been experimental evidence that entangled state collapses simultaneously?

If we observe the observable of one particle among two particles which are entangled each other and separated far away, we can determine the value of the other particle’s same observable from the ...
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Where does the negative cosine relation for quantum mechanical CHSH correlations come from?

I have been lately looking into Bell's inequality. I have noticed a recurring graph that depicts the correlation of two spins when measured at different angles, for the quantum and the classical case: ...
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How is superdeterminism a loophole to Bell's theorem?

I read wiki about superdeterminism and Bell's theorem and the lecture on free will, and I struggle to understand what free will has to do with the Bell's theorem. From my understanding, for Bell's ...
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What does the output of the correlation look like in the typical experiments testing Bell inequalities when using light and polarizers?

I am curious to know what a plot of polarizer angle vs counts produces for experimental results of Bell tests vs the classical prediction.
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Are violations of realism the same thing as contextuality?

I am basically looking for a counter-example where we'd get contextuality but not violations of realism (and vice-versa). If no such counter-examples exist, then it seems to me that they're really one ...
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How to rule out all forms of "realism"?

Thus, we see that local causality condition (1) is mathematically equivalent to the assumption of joint probabilities, $p(A_1,A_2,B_1,B_2)$. The latter is a form of realism: complementary observables ...
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Bell's theorem: why does correlation = cosine rule out hidden variables?

I was reading about entanglement and bell's theorem and played around with the idea. Specifically the point that the correlation of the measurement of entangled electrons at arbitrary angles is given ...
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Can two photons with correlated polarizations pass into a black hole and be emitted as Hawking Radiation with the correlation intact?

In this scenario photons would be emitted before they reach the centre of the black hole and before colliding with matter from a collapsed star.
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Is quantum computation possible in a superdeterministic universe?

I've seen many renowned scientists arguing that the universe is superdeterministic, but superdeterminism is a "hidden variable" theory. Is this compatible with the concept of quantum ...
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If quantum entanglement causes the violations of Bell's inequality why don't we see perfect correlation?

From wikipedia: For example, if a pair of entangled particles is generated such that their total spin is known to be zero, and one particle is found to have clockwise spin on a first axis, then the ...
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How can quantum nonlocality be understood in the path integral formalism?

I have always had my difficulties (being bored, impatient) with the theoretical considerations around quantum nonlocality, especially Bell's inequalities. What makes it cumbersome for me is that these ...
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If there is a randomness to the polarization of photons (Bell's Theorem) why radio signals hit the reciever in the same state they left the emitter? [closed]

I have tried to understand Bell's Theorem (and I am still working on that) and I am probably missing something here, but a radio signal does not seem very random, rather the opposite. It seems very ...
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When people say Bell's theorem implies either non-local realism or local non-realism, what do they mean precisely by "realism"?

From the EPR article: "If, without in any way disturbing a system, we can predict with certainty (i.e., with probability equal to unity) the value of a physical quantity, then there exists an ...
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Bell's Theorem with only two "traits"?

Every proof of Bell's Theorem I can find relies on there being three different "traits" of particles that we can choose to measure. Usually this is the spin of the particles along three ...
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Easiest way to see that superposition is necessary?

I have been discussing QM with a friend and wanted to explain why holding on to realism means we must accept non-locality. Essentially I got hung up on explaining Bell's Theorem in simple words. I ...
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Reconciling two different representations of Bell's inequality

I have a troubling question. The original Bell inequality: $$|P(\vec{a},\vec{b}) - P(\vec{a},\vec{c})| - P(\vec{b},\vec{c}) \leq 1$$ is maximally violated at angles of 60 and 120 degrees. This is ...
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Is there a Bell inequality for $2\times 2$ and $1\times1\times1\times1$ configuration?

Bell inequality is violated in entangle experiments is a known phenomenon. The standard experiment is conducted with two parties and is explained in https://en.wikipedia.org/wiki/Bell%27s_theorem#...
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What is quantum local "unrealism"?

Bell's theorem is often interpreted to have destroyed local realism. This means something like the properties of the particle do not exist until they are being measured. I am not sure what does this ...
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What if we test three photons instead of two in Bell's paradox?

I am not a physicist and do not know anything about quantum mechanics (except that it can be formulated using Hilbert spaces), but watching a vulgarization video about Bell's paradox, I had a question ...
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Bell's theorem and Fourier components

I'm looking for the error in the following because it is impossible : Bell set up the classical covariance : $$C(a,b)=\frac{1}{2\pi}\int_0^{2\pi}A(a,x)B(b,x)dx$$ Now it should have the following ...
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How does relaxing counterfactual definiteness allows for CHSH inequality violation?

Scenario, I want to play a game with a group of students as a teacher, I ask two teachers to help. The students are from the central classroom, going to room A and room B where the teachers there asks ...
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A Venn diagram for: (non-)locality, (non-)realism, (non-)contextuality, (non-)signalling, (dis-)entanglement

I recently asked a (yet-unanswered) question about the relationship between state-dependence and violations of realism. The more I read on the subject, the more I find myself digging deeper in a ...
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How can a disentangled state be contextual?

I (re-)learned about Bell tests from the ground up based on this very intuitive lecture by Spekkens. In a nutshell, realism is violated whenever measurement statistics cannot be reproduced by ...
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A discrepancy between the usual interpretation of Bell's theorem and a full theory of quantum gravity

**** This question has been modified following the discussion below. **** Bell’s theorem says, in a nutshell, that “local hidden-variable theories (HVT) cannot exist” (since they contradict QM in Bell ...
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