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Questions tagged [correlations]

In Bell test experiments, the term quantum correlation has come to mean the expectation value of the product of the outcomes on the two sides. In other words, the expected change in physical characteristics as one quantum system passes through an interaction site.

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Prove that convex combinations of product states admit a hidden variable model

Define product states as simple tensors $\rho_1 \otimes \rho_2$ and separable states to be (trace) norm limits of convex combinations of product states. We say that a state $\rho$ admits a hidden ...
truebaran's user avatar
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Why divide $\theta$ by 2 when doing the Bell's Inequality Experiment?

I understood the CHSH game correlations by watching Prof. Vazirani's video. I also understood that the correlation between two measures taken from different basis are related by the cosine of the ...
Gustavo Mirapalheta's user avatar
2 votes
1 answer
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Why are randomized strategies convex mixtures of deterministic ones?

I am looking for a proof of this fact regarding randomized strategies of the CHSH game: "... allowing randomized strategies can not help them to get a better success probability. This is because ...
NotaChoice's user avatar
1 vote
1 answer
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Can qubits be entangled without being classically corelated?

I have read before that classical correlations between qubits does not guarantee entanglement, but is the opposite also true? Consider a 3 qubit system, prepared as follows: $1-$ A Hadamard gate is ...
yousef elbrolosy's user avatar
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1 answer
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Global vs local: global density matrix and all the reduced density matrix

I prepare a $n$-qubit quantum state $\sigma$ whose ideal state is $\rho$, then perform state tomography on all the $m$- qubit reduced states. Ideally, I find that all the $m$- qubit reduced states are ...
Michael.Andy's user avatar
1 vote
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Two-time correlators in Cirq?

Is there a way to calculate two-time correlators in Cirq directly? For example, suppose we have an initial mixed state described by a density matrix $\rho_0$, and we want to obtain in our quantum ...
Zarathustra's user avatar
2 votes
1 answer
267 views

Why does measurement in computational basis result in classic probability?

I am working on a problem related to finding the limits on the joint probability distributions/correlations of three or more quantum systems who share entangled states, after measurement. I have been ...
Pegi's user avatar
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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, ...
ahelwer's user avatar
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Quantum discord of a tripartite system A:BC

I know that the quantum discord of a bipartite system can be determined as: $${D_A}({\rho _{AB}}) = I({\rho _{AB}}) - {J_A}({\rho _{AB}}),$$ The subscript of $A$ denotes that the measurement has been ...
Bekaso's user avatar
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2 votes
2 answers
189 views

Classical versus quantum correlations and partial traces

Given a bipartite state $\rho_{AB}$ living in the Hilbert space $\mathcal H(A\otimes B)$ we can always define two local states on $A$ and $B$ respectively by taking the appropriate partial traces: $$\...
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If the partial traces $\rho_A,\rho_B$ are pure, does it imply that $\rho$ is a product state?

Suppose $\rho$ is some bipartite state such that the partial traces $\rho_A={\rm Tr}_B\rho$ and $\rho_B={\rm Tr}_A\rho$ are both pure. Does this necessarily imply that $\rho$ is a product state? This ...
user15342's user avatar
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Do entangled states always result in some form of correlation?

Consider a bipartite state $\rho$, and denote with $\Pi^A\equiv \{\Pi^A_a\}_a$ and $\Pi^A\equiv\{\Pi^B_b\}_b$ local projective measurements. Let the associated joint probability distribution be $p_\Pi$...
glS's user avatar
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What is the relationship between entanglement and quantum correlation?

What is the relationship between entanglement and quantum correlation? Are they synonym? Sometimes, these two words look like synonym; people use one word to explain another, These states are not a ...
da_miao_zi's user avatar
3 votes
1 answer
78 views

$\rho_{SE}(0)=\rho_S(0)\otimes\rho_E(0)$: No coupling or no entanglement?

We know that the entangled states cannot be expressed like product state, e.g. $|\omega\rangle = |\psi\rangle\otimes|\phi\rangle$. In the density matrix describing the correlations between system $S$ ...
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How is the third-order autocorrelation measured in quantum optics?

The third order autocorrelation is defined as $$\bar g^{(3)} = \frac{\langle \hat a^\dagger \hat a^\dagger\hat a^\dagger \hat a\hat a\hat a\rangle}{\bar n^3}.$$ How is this quantity measured in ...
quest's user avatar
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Example of a two-qudit state whose measurement outcomes are independent in one basis but dependent in another

If you have a pure composite system whose two subsystems are in a product state, then the outcomes of measuring the subsystems (in any basis) are statistically independent. If the subsystems are ...
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Quantum Ising model correlation function query

In this paper on quantum Ising model dynamics, they consider the Hamiltonian $$\mathcal{H} = \sum_{j < k} J_{jk} \hat{\sigma}_{j}^{z}\hat{\sigma}_{k}^{z}$$ and the correlation function $$\mathcal{G}...
John Doe's user avatar
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2 votes
1 answer
108 views

Can pairwise entanglement be converted into tripartite correlations?

Suppose Alice shares $m$ pairs of maximally entangled states with Bob and $n$ pairs of maximally entangled states with Charlie. It is clear that by measuring their states, Alice can generate ...
user1936752's user avatar
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Out-of-time-order correlation function in the interaction picture?

Recently there has been interest in understanding the out of time order correlation function (OTOC) $F$, which essentially compares the overlap of two operators $W$ and $V$ acting on a state in two ...
Dr. T. Q. Bit's user avatar
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General Master Equation with Decoherence Query

The following general master equation (from this paper 'Dynamical quantum correlations of Ising models on arbitrary lattice and their resilience to decoherence') describes the various types of ...
John Doe's user avatar
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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,...
The Bosco's user avatar
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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} + ...
Bob's user avatar
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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 ...
Sanchayan Dutta's user avatar
1 vote
1 answer
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Why is correlation in the $X$ basis represented as $X\otimes X = 1$?

As far as I know, correlation of two qubits in the $X$ basis implies that under a simultaneous bit flip, the composite quantum state must be invariant. For instance, $A$ and $B$ can be said to be ...
Sanchayan Dutta's user avatar
5 votes
1 answer
141 views

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 $x,y \in \{0, 1\}$ ...
ahelwer's user avatar
  • 4,138
6 votes
1 answer
242 views

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 &...
ahelwer's user avatar
  • 4,138
6 votes
2 answers
480 views

In Bell nonlocality, why does $P(ab|xy)\neq P(a|x)P(b|y)$ mean the variables are not statistically independent?

I've been working through the paper Bell nonlocality by Brunner et al. after seeing it in user glS' answer here. Early on in the paper, the standard Bell experimental setup is defined: Where $x, y \...
ahelwer's user avatar
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13 votes
3 answers
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Are correlations stronger than those allowed by quantum mechanics possible?

We know how a quantum correlation setup can help us with a better probability of winning games like the CHSH. But what is the upper bound that physics can allow? Is it the quantum correlation setup? ...
Siddhant Singh's user avatar
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2 answers
4k views

How are EPR Pairs used in quantum computing?

Context Lately, I have been reading a scholarly paper entitled An Introduction to Quantum Computing for Non-Physicists which discusses the EPR Paradox. The paper states that: Einstein, Podolsky ...
Daniel Burkhart's user avatar
5 votes
1 answer
3k views

What is the difference between signaling and non-signaling quantum correlations, and what is a signaling channel?

This article talks about correlation and causality in quantum mechanics. In the abstract, under Framework for local quantum mechanics, it says (emphasis mine): The most studied, almost epitomical, ...
fr_andres's user avatar
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