Questions tagged [bell-experiment]
For questions on Bell test experiments or Bell's inequality experiments, including but not limited to the CHSH and CH74.
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How can I simulate EPR and Bell’s inequalities in qiskit?
According to Bernard Zygelman "A First Introduction to Quantum Computing and Information", I can compute the $QS|f\rangle$ with $|f\rangle = \frac{1}{\sqrt{2}} (|00\rangle -|11\rangle)$, ...
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Verifying equation 4 in Ekert's paper "Quantum Cryptography Based on Bell's Theorem"
Ekert's 1999 paper (link to download) cites the classic CHSH paper on generalized Bell inequality and says
(2) $E(a,b)=-a\cdot b$
(3) $S = E(a_1,b_1)-E(a_1,b_3)+E(a_3,b_1)_E(a_3,b_3)$
(4) $S = -2\sqrt(...
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Quantinuum corporation says they have a Bell test for quantum randomness. Why does the simulator pass the test?
I'm researching the quantum random number service offered by the computer maker Quantinuum. They say that they have verified quantum randomness by a Bell test. I took Bell's 1964 classic paper and ...
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Spreading entanglement over multiple systems
Question: imagine that Alice and Bob share, say, one ebit $\lvert\Phi_+\rangle_\text{AB}$, and that they are only able to carry out local operations and classical communication. Is there an algorithm ...
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Worst Bell inequality violation with non-maximally entangled state?
I'm familiar with CHSH game and the strategy that allows Alice and Bob to succeed with a probability of $$\frac{1+\tfrac{1}{\sqrt 2}}{2}\approx 85\%$$ if they share a maximally entangled state such as ...
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Is it advantageous for a state to have higher Bell CHSH violation?
For a density matrix $\hat \rho$, one can construct a "Bell operator" $\hat B$, such that the violation of the inequality $\langle \hat B \rangle \le 2$ is a clear indication of quantum ...
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Why only one of the qubits is rotated in the CHSH circuit?
When reading various tutorials on how to calculate CHSH, there is only a single qubit which is rotated inside of the quantum circuit, it is also only ever rotated around a single axis.
I would like to ...
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The Ekert Protocol (E91) for Quantum Key Distribution
My question is specifically from the book Quantum Computing for Everyone by Chris Bernhardt.
In the last section (The Ekert Protocol for Quantum Key Distribution) from Chapter 5 (Bell's Inequality). I ...
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Choosing operators for maximal Bell-CHSH violation for an arbitrary state
If I have the density matrix $\rho$ for a bipartite system (each system is two-dimensional), what set of observables should I choose so that I obtain the maximum possible violation of the Bell-CHSH ...
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What are the 2022 Nobel Prize winning papers of Alain Aspect, John Clauser, and Anton Zeilinger, and how do they fit into the timeline of QIS?
The 2022 Nobel Prize in Physics was awarded to Alain Aspect, John Clauser, and Anton Zeilinger for "experiments with entangled photons... pioneering quantum information science".
Presumably ...
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XOR game quantum strategy expected payoff?
I am reading Thomas Vidick, Quantum multiplayer games, testing and rigidity. On top of p.4,
$$\text{E}[a\cdot b] = \sum_{i,j\in \{0,1\}}(-1)^{i+j}\text{Pr}\big((a,b)=(i,j)\big)$$
I do not understand ...
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QKD + CHSH inequality
CHSH inequality has been used all over the QKD protocols to test the presence of Eve.
Let us assume we have sent N qubits and k out the N will be used to the test (CHSH). What is the minimum K ...
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What's wrong with this simplified Bell experiment? [closed]
This code is supposed to be sending two oppositely-entangled qubits to two measuring devices. Each measuring device chooses one of three angles at random. with the three angles being 120 degrees apart....
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What is the difference between $|\Phi^+\rangle=\frac1{\sqrt2}(|0,0\rangle+|1,1\rangle)$ and a mixture of $|00\rangle$ and $|11\rangle$?
I struggle to see the difference between $|\Phi^+\rangle = \frac{1}{\sqrt{2}} (|0\rangle_A \otimes |0\rangle_B + |1\rangle_A \otimes |1\rangle_B)$ and the mixed state defined with probabilities {0.5, ...
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Bell test results question
I created two Qiskit programs to do a Bell test for hidden variables. In one test, the program does 100 shots for each of nine circuits -- a total of 900 shots. The result is always close to 0.50 as ...
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What is the no-signaling set and how can it be related to other types of correlations?
The paper Bell nonlocality by Brunner et. al includes a striking diagram on page 7:
This is fascinating to me because it suggests a framework of categorizing correlations that encompasses classical, ...
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What is an example of an entangled state whose correlations are describable with a local hidden variable model?
When talks about CHSH inequality, we always say that the states that violate the inequality are entangled, while some states that do not violate the inequality can also be entangled.
For the latter ...
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Bell's experiment: checking the probabilities
I have some doubts on the calculations behind Bell's experiment, which goes as follows: a pair of entangled photons is shared between two scientists, Alice and Bob, who possess a bunch of polarizers ...
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EPR pair and individual operations [closed]
I have created an EPR pair. Let's suppose it's $(|00\rangle + |11\rangle)/\sqrt{2}$. We both of our halves and then we move into our places.
If I ask you how does your half look like (mathematical ...
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In Bell's inequalities, what is the meaning of assuming that the physical properties $P_Q,P_R,P_S,P_T$ have definite values?
Two assumptions behind Bell inequalities (Page 117 Nielsen Chuang)
(1) The assumption that the physical properties $P_{Q}$, $P_{R}$, $P_{S}$, $P_{T}$ have definite values
$Q$,$R$, $S$, $T$ which exist ...
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Formal proof of Bell's inequality in CHSH form
I have a sketch of the proof of Bell's theorem that goes as follows: Alice measures an observable $A$ along a direction $\vec a$ with possible outcomes $\pm 1$, and Bob does the same for an observable ...
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Modified CHSH game - Does entanglement help?
I'm thinking about a modified version of the CHSH game and I'm trying to convince myself that in this case, entanglement cannot be used to gain an advantage or else it would imply signalling is ...
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How can I measure a qubit on a generic axis on Qiskit?
I'm trying to prove Bell's inequality by following the one made by Wigner, that is:
$P(+_a,+_b) \le P(+_a,+_c) + P(+_c,+_b)$
And that this proof is NOT satisfied for angles between the various axes $\...
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Output of Bell State Measurement
I was trying to see the output of Bell State Measurement in IBM Quantum Experience but in the simulation down the circuit in the histogram, it showed me that the possible qubit will be $|00\rangle$ ...
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Difference between Bell's inequality and CHSH
In this section of the Scholarpedia article on Bell's theorem, the first paragraph comments that Bell's original inequality is not ideal for experimental verification because it requires perfect anti-...
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Where does $xy = a + b \pmod 2$ come from in the context of CHSH inequalities?
I have been looking into the great! video lecture of "CSHS Inequality" by Prof. Umesh V. Vazirani.
There are a few things I have to clarify, hope someone will answer me.
Suppose Alice and ...
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Is this a Bell test?
Inspired by this article which uses a $|+\rangle$ state as a control for a $CSWAP$, I realised you can conditionally measure a qubit by (maybe) swapping it with an empty ancilla, measuring it and (...
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What is the analysis of the Bell Inequality protocol in Cirq's 'examples'?
This question is taken from https://github.com/quantumlib/Cirq/issues/3032.
The "standard" protocol measures Alice's and Bob's qubits in different bases, while the one in Cirq measures in ...
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Problem about entanglement swapping
I have been learning about the concept of entanglement swapping and found an equation mentioned in the textbook, Mathematics Of Quantum Computing: An Introduction written by Wolfgang Scherer.
At ...
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How to prepare an arbitrary two-qubit state?
I know that to prepare a Bell state say $|\phi^+\rangle$, we need to initial state $|0\rangle,|0\rangle$ and then perform a Hadamard on the first and then use it as control to do a NOT gate on the ...
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What would the CHSH inequality be equal to if the two qubits were separable?
I am writing an Excel spreadsheet to work through the matrix algebra for a simple Bell's game with the following parameters.
$$\newcommand{\bra}[1]{\langle #1|}\newcommand{\ket}[1]{|#1\rangle}A_\pm = ...
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What are the two measurements per box being done in the Bell Tests in the IBM Quantum Experience "Entanglement and Bell tests" Section
I am confused as to what is being measured in the boxes in the example drawings shown on the Entanglement and Bell Tests section in the IBM Q Experience:
https://quantum-computing.ibm.com/docs/guide/...
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Why is the CHSH inequality defined with a minus sign?
CHSH inequality is defined in the following way. Let $Q, R, S, T$ be two outcomes $\{\pm 1\}$ measurements. The measurements are chosen in a certain way, but that is not our concern right now. We know ...
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What is the number of local deterministic behaviours in a Bell scenario?
Consider a Bell scenario: Alice and Bob perform measurements on a shared system, and each of them has a "measurement box" with a bunch of inputs (corresponding to different measurement settings) and ...
glS♦
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Does the CHSH inequality fully characterise the local polytope?
Consider the standard two-party CHSH scenario. Each party can perform one of two measurements (denoted with $x,y\in\{0,1\}$) and observe one of two outcomes (denoted with $a,b\in\{0,1\}$).
Let $P(ab|...
glS♦
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Are there Bell-like violations that can be observed without collecting statistics?
Observing the violation of Bell inequalities, be it in their original formulation, or in the nowadays more commonly used CHSH formulation, involves computing averages of specific experimentally ...
glS♦
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Find the Bell States of A and B in the following scenario
Let A has quantum memories $M_1$ and $M_2$ and B has quantum memories $M_3$ and $M_4$ capable of holding one qubit.
2 Bell states are shared among A & B in the following way:
First Bell state $|...
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given an EPR pair, how do I calculate expectation value?
given A and B share EPR pairs $ (|00⟩+|11⟩)/√2$
both are free to measure their own qubit with the following measurement settings
A measures with $[ |0⟩, |1⟩ ]$
B measures with $[ sin(3π/8)|0⟩ + cos(...
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Projecting $\lvert ++ \rangle$ on Bell Basis
I understand that, projecting $\lvert 00\rangle$ on the Bell states would produce $\lvert\Phi^+\rangle$. Because,
$$
CNOT(H\lvert0\rangle \otimes \lvert0\rangle) = \frac{1}{\sqrt{2}}(\lvert00\rangle +...
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Bell State 11 not working for parity curve
I am currently writing a script to automate the creation of parity curves for a 2 qubit bell state and then calculate fidelity and proving entanglement from that (inspired by this paper). It was going ...
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Simultaneous eigenstate of commuting observables and their tensor product
So this is about something from Preskill's notes on Quantum Computation and Information, Chapter 4, page 3.
Imagine we have a maximally entangled state (Bell state). We can identify the Bell state by ...
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How to measure a Bell inequality violation in IBM Q?
Note: Cross-posted on Physics SE.
I made some circuit to prepare a 2 qubit state, but I am having trouble understanding how to measure Bell's inequality. I know the inequality is of the form
$$|E(a,...
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How is Bell’s Inequality converted to the CHSH inequality?
Bell’s inequality is $$S = P(a,b)-P(a,d)+P(c,b)+P(c,d) \leq 2,$$ which is calculated as $$S = ab – ad + cb + cd \leq 2.$$
The CHSH version is:
$$E = \frac{N_{11} + N_{00} - N_{10} -N_{01}} {N_{11} + ...
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Why is $P(1,2)_{\text{same}} = \frac{1}{4}$ and not $\frac{1}{2}$ in Preskill's Bell experiment?
Context:
Three coins on the table. Each is either heads or tails. You can
uncover any one of the three coins, revealing whether it is heads or
tails but then you choose two the other two coins ...
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Determining whether $P(ab|xy)$ factorizes in Bell experiments
Continuing from my previous (1, 2) questions on Brunner et al.'s paper on Bell nonlocality.
Again, we have the following standard Bell experiment setup:
where independent inputs $x,y \in \{0, 1\}$ ...
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Definition of locality in Bell experiments
Continuing from my previous question on Brunner et al.'s paper; so given a standard Bell experimental setup:
where independent inputs $x,y \in \{0, 1\}$ decide the measurement performed by Alice &...
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References examining Bell inequality violations at large distances
Could anyone point to some references examining Bell inequality violations at large distances please?
I see many times, in pop science articles and research literature alike, that the quantum ...
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How would a Quantum Computer (network) perform loophole-free Bell tests?
In a simple form, Bell's theorem states that:
No physical theory of local hidden variables can ever reproduce all of the predictions of quantum mechanics.
Bell developed a series of inequalities ...
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