Quantum Coupling and Strassen Theorem

03/28/2018

∙

by   Li Zhou, et al.

∙

0

∙

share

We introduce a quantum generalisation of the notion of coupling in probability theory. Several interesting examples and basic properties of quantum couplings are presented. In particular, we prove a quantum extension of Strassen theorem for probabilistic couplings, a fundamental theorem in probability theory that can be used to bound the probability of an event in a distribution by the probability of an event in another distribution coupled with the first.