Equivalence between divisibility and monotonic decrease of information in classical and quantum stochastic processes

Abstract

The crucial feature of a memoryless stochastic process is that any information about its state can only decrease as the system evolves. Here we show that such a decrease of information is equivalent to the underlying stochastic evolution being divisible. The main result, which holds for both classical and quantum stochastic processes, rely on a quantum version of the so-called Blackwell-Sherman-Stein theorem in classical statistics.

v3: published version. v2: extensive revision, lot of references added, same results. v1: 5+2 pages, 1 figure