Equivalence between divisibility and monotonic decrease of information in classical and quantum stochastic processes
arXiv:1408.7062 · doi:10.1103/PhysRevA.93.012101
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
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