In
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 chemistr ...
, 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
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 e ...
, 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 N
total, 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
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 or
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.
See also
*
Correlation does not imply causation
*
EPR paradox
EPR may refer to:
Science and technology
* EPR (nuclear reactor), European Pressurised-Water Reactor
* EPR paradox (Einstein–Podolsky–Rosen paradox), in physics
* Earth potential rise, in electrical engineering
* East Pacific Rise, a mid-oc ...
References
* J. S. Bell, Speakable and Unspeakable in Quantum Mechanics, (Cambridge University Press 1987)
Correlation
{{quantum-stub