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

Canturk B.

Annals of Physics, cilt.487, 2026 (SCI-Expanded, Scopus) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 487
  • Basım Tarihi: 2026
  • Doi Numarası: 10.1016/j.aop.2026.170367
  • Dergi Adı: Annals of Physics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Chemical Abstracts Core, INSPEC, MathSciNet, zbMATH
  • Anahtar Kelimeler: Chapman–Kolmogorov equation, Markovianity, Quantum Markovianity, Quantum operations, Quantum processes, Stochastic processes
  • İstanbul Gelişim Üniversitesi Adresli: Evet

Özet

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.