quantum correlations

Quantum correlations are the statistical links between the outcomes of measurements on entangled particles — links that can be stronger than any classical theory allows. If you measure many entangled pairs and tabulate how often the two sides agree as you vary the measurement settings, the pattern you get cannot be matched by any account in which each particle carried its answers locally in advance. The correlations themselves, not any single result, are where the quantumness lives.

It helps to see the spectrum they sit on. Ordinary classical correlations, like two cards drawn from a shuffled deck, can be strong but obey Bell's bound. Quantum correlations overshoot that bound, reaching up to the so-called Tsirelson limit. Curiously, they do not go all the way to the most extreme imaginable correlations: nature permits more than classical physics but less than logic alone would allow, and why it stops exactly where it does is still an open question.

These correlations are not just a curiosity; they are a resource. The certified randomness in them powers protocols whose security does not depend on trusting the hardware, and their strength is what makes quantum key distribution and other quantum-information tasks possible. Yet for all their power they remain perfectly disciplined: each side alone sees only noise, so the correlations enrich what two parties can do together without ever letting either one signal to the other faster than light.