quantum mechanics Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, q ...

, quantum correlation is the

expected value In probability theory, the expected value (also called expectation, expectancy, mathematical expectation, mean, average, or first moment) is a generalization of the weighted average. Informally, the expected value is the arithmetic mean of a ...

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 A Bell test, also known as Bell inequality test or Bell experiment, is a real-world physics experiment designed to test the theory of quantum mechanics in relation to Albert Einstein's concept of local realism. Named for John Stewart Bell, the ex ...

, 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 :

\frac

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 N_total, it is customary to divide by :

N_  + N_+ N_ + N_

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 :

QC(a, b) = \int d \lambda \rho (\lambda) A(a, \lambda)B(b, \lambda)

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 A statistic (singular) or sample statistic is any quantity computed from values in a sample which is considered for a statistical purpose. Statistical purposes include estimating a population parameter, describing a sample, or evaluating a hy ...

in the

CHSH inequality In physics, the CHSH inequality can be used in the proof of Bell's theorem, which states that certain consequences of entanglement in quantum mechanics can not be reproduced by local hidden-variable theories. Experimental verification of the i ...

and some of the other Bell inequalities, tests that open the way for experimental discrimination between quantum mechanics and

local realism In physics, the principle of locality states that an object is influenced directly only by its immediate surroundings. A theory that includes the principle of locality is said to be a "local theory". This is an alternative to the concept of ins ...

local hidden-variable theory In the interpretation of quantum mechanics, a local hidden-variable theory is a hidden-variable theory that satisfies the condition of being consistent with local realism. This includes all types of the theory that attempt to account for the proba ...

Outside Bell test experiments

Quantum correlations give rise to various phenomena, including interference of particles separated in time.

References

* J. S. Bell, Speakable and Unspeakable in Quantum Mechanics, (Cambridge University Press 1987)

Correlation In statistics, correlation or dependence is any statistical relationship, whether causal or not, between two random variables or bivariate data. Although in the broadest sense, "correlation" may indicate any type of association, in statisti ...

{{quantum-stub

Outside Bell test experiments

See also

References