Dynamics beyond completely positive maps: Some properties and applications

2005/12/31 by Hilary A. Carteret, Hilary Carteret, Daniel R. Terno +2 · 12 citations
Computer Science · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Quantum Information and Cryptography #Quantum Mechanics and Applications #quant-ph

paper · pdf · doi:10.1103/physreva.77.042113

published as Phys. Rev A 77, 042113 (2008) · 8 pages, 1 eps figure. Final version

openalex publication_date 2008/04/18 · arxiv created 2008/04/20 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30

Abstract

Maps that are not completely positive (CP) are often useful to describe the dynamics of open systems. An apparent violation of complete positivity can occur because there are prior correlations of the principal system with the environment, or if the applied transformation is correlated with the state of the system. We provide a physically motivated definition of accessible non-CP maps and derive two necessary conditions for a map to be accessible. We also show that entanglement between the system and the environment is not necessary to generate a non-CP dynamics. We describe two simple approximations that may be sufficient for some problems in process tomography, and then outline what these methods may be able to tell us in other situations where non-CP dynamics naturally arise.

Citations

• Separability Criterion for Density Matrices
• Non-Markovian generalization of the Lindblad theory of open quantum systems
• Completely positive linear maps on complex matrices

Cited by

• Initial correlations in open-systems dynamics: The Jaynes-Cummings model
• Quartic quantum theory: an extension of the standard quantum mechanics
• Linear assignment maps for correlated system-environment states
• Completely positive maps and classical correlations
• Vanishing quantum discord is not necessary for completely positive maps
• Repeatable quantum memory channels
• Operational approach to open dynamics and quantifying initial correlations
• Unitary–scaling decomposition and dissipative behaviour in finite-dimensional unital Lindblad dynamics
• The Information Recovery Problem
• Equilibration and Typicality in Quantum Processes
• Purity as a witness for initial system-environment correlations in open-system dynamics
• Effects of initial system-environment correlations on open-quantum-system dynamics and state preparation