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arXiv · 2503.09333

Unification of stochastic matrices and quantum operations for N-level systems

Bilal Canturk
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Abstract

The time evolution of the one-point probability vector of stochastic processes and quantum processes for $N$-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.

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Bilal Canturk. 2025-03-12. Unification of stochastic matrices and quantum operations for N-level systems. https://doi.org/10.1016/j.aop.2026.170367

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