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Equivalence between divisibility and monotonic decrease of information in classical and quantum stochastic processes
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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.
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Divisible and indivisible Stochastic-Quantum dynamics
A two-state stochastic evolution is divisible between given times if and only if the earlier transition matrix lies in one of two explicitly described cone regions, with continuous curves crossing a critical diagonal ...
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