Unification of stochastic matrices and quantum operations for N-level systems
Annals of Physics, vol.487, 2026 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 487
- Publication Date: 2026
- Doi Number: 10.1016/j.aop.2026.170367
- Journal Name: Annals of Physics
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Chemical Abstracts Core, INSPEC, MathSciNet, zbMATH
- Keywords: Chapman–Kolmogorov equation, Markovianity, Quantum Markovianity, Quantum operations, Quantum processes, Stochastic processes
- Istanbul Gelisim University Affiliated: Yes
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.