Completely Positive Divisibility Does Not Mean Markovianity

2019/01/31 by Simon Milz, M. S. Kim, Felix A. Pollock +1 · 3 citations
Computer Science · Mathematics · Physics and Astronomy · #Combinatorics #Computability, Logic, AI Algorithms #Divisibility rule #Mathematics #Physics #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Statistical physics #Statistics #quant-ph

paper · pdf · doi:10.1103/physrevlett.123.040401

published as Phys. Rev. Lett. 123, 040401 (2019) · 4+5 pages, 4 figures, close to published version

openalex publication_date 2019/07/22 · arxiv created 2019/08/05 · arxiv updated 2019/08/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

In the classical domain, it is well known that divisibility does not imply that a stochastic process is Markovian. However, for quantum processes, divisibility is often considered to be synonymous with Markovianity. We show that completely positive divisible quantum processes can still involve non-Markovian temporal correlations, that we then fully classify using the recently developed process tensor formalism, which generalizes the theory of stochastic processes to the quantum domain.

Citations

• Quantum Circuit Architecture
• Stochastic Dynamics of Quantum-Mechanical Systems
• Dividing Quantum Channels
• Inferring statistical complexity
• Completely positive linear maps on complex matrices
• Thermalizing Quantum Machines: Dissipation and Entanglement
• Divisible quantum dynamics satisfies temporal Tsirelson’s bound
• Concepts of quantum non-Markovianity: a hierarchy
• Quantum Computing in the NISQ era and beyond

Cited by

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• Equilibration and Typicality in Quantum Processes
• Open system dynamics from thermodynamic compatibility