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Concept# Quantum correlation

Summary

In quantum mechanics, quantum correlation is the expected value of the product of the alternative outcomes. In other words, it is the expected change in physical characteristics as one quantum system passes through an interaction site. In John Bell's 1964 paper that inspired the Bell test, it was assumed that the outcomes A and B could each only take one of two values, -1 or +1. It followed that the product, too, could only be -1 or +1, so that the average value of the product would be
where, for example, N++ is the number of simultaneous instances ("coincidences") of the outcome +1 on both sides of the experiment.
However, in actual experiments, detectors are not perfect and produce many null outcomes. The correlation can still be estimated using the sum of coincidences, since clearly zeros do not contribute to the average, but in practice, instead of dividing by Ntotal, it is customary to divide by
the total number of observed coincidences. The legitimacy of this method relies on the assumption that the observed coincidences constitute a fair sample of the emitted pairs.
Following local realist assumptions as in Bell's paper, the estimated quantum correlation converges after a sufficient number of trials to
where a and b are detector settings and λ is the hidden variable, drawn from a distribution ρ(λ).
The quantum correlation is the key statistic in the CHSH inequality and some of the other Bell inequalities, tests that open the way for experimental discrimination between quantum mechanics and local realism or local hidden-variable theory.
Quantum correlations give rise to various phenomena, including interference of particles separated in time.

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Quantum correlation

In quantum mechanics, quantum correlation is the expected value of the product of the alternative outcomes. In other words, it is the expected change in physical characteristics as one quantum system passes through an interaction site. In John Bell's 1964 paper that inspired the Bell test, it was assumed that the outcomes A and B could each only take one of two values, -1 or +1. It followed that the product, too, could only be -1 or +1, so that the average value of the product would be where, for example, N++ is the number of simultaneous instances ("coincidences") of the outcome +1 on both sides of the experiment.

Hidden-variable theory

In physics, hidden-variable theories are proposals to provide explanations of quantum mechanical phenomena through the introduction of (possibly unobservable) hypothetical entities. The existence of fundamental indeterminacy for some measurements is assumed as part of the mathematical formulation of quantum mechanics; moreover, bounds for indeterminacy can be expressed in a quantitative form by the Heisenberg uncertainty principle.

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