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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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 ...
6 votes
1 answer
187 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 &...
5 votes
1 answer
122 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 $x,y \in \{0, 1\}$ ...
2 votes
1 answer
70 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 ...
7 votes
2 answers
106 views

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, ...
3 votes
1 answer
112 views

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 ...
2 votes
2 answers
100 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: $$\...
4 votes
1 answer
145 views

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 ...
3 votes
1 answer
102 views

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 $p_\Pi$...
3 votes
0 answers
114 views

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 ...
3 votes
2 answers
1k views

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} + ...
5 votes
1 answer
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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, ...
9 votes
2 answers
375 views

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? ...
3 votes
1 answer
60 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 $S$ ...
1 vote
0 answers
59 views

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 ...
3 votes
1 answer
64 views

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 ...
6 votes
2 answers
408 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 \...
3 votes
0 answers
76 views

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 ...
3 votes
2 answers
117 views

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 ...
3 votes
0 answers
64 views

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}...
2 votes
1 answer
63 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 ...
3 votes
0 answers
463 views

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,...
1 vote
1 answer
79 views

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 ...
3 votes
2 answers
3k 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 ...