Unification of stochastic matrices and quantum operations for N-level systems
arXiv:2503.09333 · doi:10.1016/j.aop.2026.170367
Abstract
The time evolution of the one-point probability vector of stochastic processes and quantum processes for -level systems have been unified. Hence, quantum states and quantum operations can be regarded as generalizations of the one-point probability vectors and stochastic matrices, respectively. More essentially, based on the unification, it has been proven that completely positive divisibility (CP-divisibility) for quantum operations is the natural extension of the Chapman-Kolmogorov equation. It is thus shown that CP-divisibility is a necessary but insufficient condition for a quantum process to be specified as Markovian. The main results have been illustrated through a dichotomic Markov process.
11 pages, 1 figure, research paper
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