Zero-correlation entanglement. (13th January 2020)

• Record Type: Journal Article
• Authors: Ohira, Toru
• Is Part Of: Progress of theoretical and experimental physics. Volume 2020:Number 1(2020)
• Publication Date: 2020-01-13
• Subjects: A60; Physics -- Periodicals; Mathematical physics -- Periodicals; 530.05
• DOI: 10.1093/ptep/ptz149
• Languages: English
• ISSNs: 2050-3911

Abstract

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 $\mathcal{X}, \mathcal{Y}$ with zero correlations ($\langle{\psi}|\mathcal{X}\mathcal{Y}|{\psi}\rangle - \langle{\psi}|\mathcal{X}|{\psi}\rangle\langle{\psi}|\mathcal{Y}|{\psi}\rangle= 0$ ). 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.