Zero-Correlation 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.
Cite
@article{arxiv.1909.01343,
title = {Zero-Correlation Entanglement},
author = {Toru Ohira},
journal= {arXiv preprint arXiv:1909.01343},
year = {2020}
}
Comments
11 pages, Discussion on the quantum pigeonhole effect and references added in version 2; Extension to mixed states is added in the appendix in version 3 (The appendix is not included in the published version in PTEP)