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

TL;DR

This paper demonstrates that in both classical and quantum stochastic processes, the decrease of information over time is equivalent to the process being divisible, linking information dynamics to process structure.

Contribution

It establishes a fundamental equivalence between information decrease and divisibility in classical and quantum stochastic processes, using a quantum extension of a classical statistical theorem.

Findings

Information decrease implies process divisibility.

Divisibility of processes ensures monotonic information loss.

The results unify classical and quantum stochastic process theories.

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.