Depolarizing channel as a completely positive map with memory

2003/09/09 by Sonja Daffer, Krzysztof Wódkiewicz, Krzysztof Wodkiewicz +3 · 6 citations
Computer Science · Mathematics · Physics and Astronomy · #Applied mathematics #Dissipative system #Exponential function #Kernel (algebra) #Master equation #Mathematical analysis #Mathematics #Physics #Pure mathematics #Quantum #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum mechanics #Quantum optics and atomic interactions #Quantum state #Statistical physics #Statistics #TRACE (psycholinguistics) #Trace distance #White noise #quant-ph

paper · pdf · doi:10.1103/physreva.70.010304

published as Phys. Rev. A 70, 010304 (2004) · 4 pages

arxiv created 2003/09/09 · openalex publication_date 2004/07/21 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

The prevailing description for dissipative quantum dynamics is given by the Lindblad form of a Markovian master equation, used under the assumption that memory effects are negligible. However, in certain physical situations, the master equation is essentially of a non-Markovian nature. In this paper we examine master equations that possess a memory kernel, leading to a replacement of white noise by colored noise. The conditions under which this leads to a completely positive, trace-preserving map are discussed for an exponential memory kernel.

Citations

• Completely positive dynamical semigroups of N-level systems
• Stochastic Processes in Physics and Chemistry

Cited by

• Estimating the degree of non-Markovianity using machine learning
• Characterizing qubit channels in the context of quantum teleportation
• Non-Markovian quantum dynamics and classical chaos
• Non-Markovian dynamics of a qubit
• On the indistinguishability of Raman photons
• Open system dynamics from thermodynamic compatibility