Zero-Correlation Entanglement

TL;DR

This paper demonstrates that quantum entangled states can have zero correlations between certain observables, unlike classical entangled systems, highlighting a fundamental difference between quantum and classical correlations.

Contribution

It proves that quantum entangled states can exhibit zero correlations with specific observables, contrasting with classical systems where zero correlation is impossible.

Findings

Quantum entangled states can have zero correlations between certain observables.

Classical entangled (non-independent) variables cannot have zero correlations.

The paper provides a general proof distinguishing quantum and classical entanglement.

Abstract

We consider a quantum entangled state for two particles, each particle having two basis states, which includes an entangled pair of spin 1/2 particles. We show that, for any quantum entangled state vectors of such systems, one can always find a pair of observable operators X, Y with zero-correlations <XY> = <X><Y>. At the same time, if we consider the analogous classical system of a "classically entangled" (statistically non-independent) pair of random variables taking two values, one can never have zero correlations (zero covariance, E[XY] - E[X]E[Y] = 0). We provide a general proof to illustrate the different nature of entanglements in classical and quantum theories.