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

• URL: http://arxiv.org/abs/2503.09333v1
• Date: Wed, 12 Mar 2025 12:27:39 GMT
• Title: Unification of stochastic matrices and quantum operations for N-level systems
• Authors: Bilal Canturk,
• Abstract summary: Time evolution of one-point probability distribution processes and quantum processes for $N$-level systems has been unified.<n> quantum states and quantum operations can be regarded as generalizations of the one-point probability vectors and matrices.<n>CP-divisibility is a necessary but insufficient condition for a quantum process to be specified as Markovian.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: The time evolution of the one-point probability distribution of stochastic processes and quantum processes for $N$-level systems has been unified. Hence, quantum states and quantum operations can be regarded as generalizations of the one-point probability vectors and stochastic matrices, respectively. It has also 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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