English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

It is well known that when a pair of random variables is statisticallyindependent, 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 variablestake only two values, no-correlation entails statistical independence. Weprovide here a general proof. We subsequently examine whether this equivalenceproperty carries over to quantum mechanical systems. A counter-example isexplicitly constructed to show that it does not. This observation provides yetanother simple theorem separating classical and quantum theories.

On Statistical Independence and No-Correlation for a Pair of Random Variables Taking Two Values: Classical and Quantum