Quantum Coupling and Strassen Theorem

TL;DR

This paper introduces a quantum generalization of probabilistic coupling, extending Strassen's theorem to quantum settings, which could impact quantum probability and information theory.

Contribution

It presents the first quantum extension of Strassen's theorem, broadening the theoretical framework of quantum couplings and their properties.

Findings

Defined quantum couplings and explored their properties

Proved a quantum version of Strassen's theorem

Provided examples illustrating the quantum coupling concept

Abstract

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.