Quantum correlation

Key takeaways

Quantum correlation belongs to physics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Quantum correlation to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Quantum correlation from memory before moving on to harder problems.

Reference excerpt

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

N + + − N + − − N − + + N − − N t o t a l {\displaystyle {\frac {N_{++}-N_{+-}-N_{-+}+N_{--}}{N_{total}}}}

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

N + + + N + − + N − + + N − − {\displaystyle 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

Q C ( a , b ) = ∫ d λ ρ ( λ ) A ( a , λ ) B ( b , λ ) {\displaystyle 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 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.

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

References

J. S. Bell, Speakable and Unspeakable in Quantum Mechanics, (Cambridge University Press 1987) ISBN 0-521-52338-9

Worked examples

Example 1 — a first encounter with Quantum correlation

Start with the simplest possible case. Write down what Quantum correlation claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In physics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Quantum correlation before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Quantum correlation ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Quantum correlation

In research: Quantum correlation appears in physics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Quantum correlation in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Quantum correlation is common in secondary-school and first-year university syllabi. It links to neighbouring topics Quantum measurement, Quantum physics stubs, so understanding it makes those chapters shorter.
In everyday life: Look for Quantum correlation outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

How to study Quantum correlation in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Quantum correlation means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Quantum correlation out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Quantum correlation in simple terms?

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.

Why does Quantum correlation matter?

Because it connects several physics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Quantum correlation?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Quantum correlation.