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| Format: | Preprint |
| Published: |
2025
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| Online Access: | https://arxiv.org/abs/2503.09333 |
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| _version_ | 1866910006939484160 |
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| author | Canturk, Bilal |
| author_facet | Canturk, Bilal |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_09333 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Unification of stochastic matrices and quantum operations for N-level systems Canturk, Bilal Quantum Physics 81P45, 81P05, 60G07 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. |
| title | Unification of stochastic matrices and quantum operations for N-level systems |
| topic | Quantum Physics 81P45, 81P05, 60G07 |
| url | https://arxiv.org/abs/2503.09333 |