On statistical independence and no-correlation for a pair of random variables taking two values: Classical and quantum. (21st August 2018)

• Record Type: Journal Article
• Authors: Ohira, Toru
• Is Part Of: Progress of theoretical and experimental physics. Volume 2018:Number 8(2018)
• Publication Date: 2018-08-21
• Subjects: A60; Physics -- Periodicals; Mathematical physics -- Periodicals; 530.05
• DOI: 10.1093/ptep/pty086
• Languages: English
• ISSNs: 2050-3911

Abstract

Abstract: It is well known that when a pair of random variables is statistically independent, it has no-correlation (zero covariance, $E[XY] - E[X]E[Y] = 0$ ), and that the converse is not true. However, if both of these random variables take only two values, no-correlation entails statistical independence. We provide here a general proof. We subsequently examine whether this equivalence property carries over to quantum mechanical systems. A counter-example is explicitly constructed to show that it does not. This observation provides yet another simple theorem separating classical and quantum theories.