  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.

Quantum Physics;Logic in Computer Science