Reduced Dynamics Need Not Be Completely Positive

1994/08/22 by Philip Pechukas · 23 citations
Computer Science · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Computer science #Dynamics (music) #Extension (predicate logic) #Geometry #Linearity #Mathematics #Physics #Positive feedback #Product (mathematics) #Quantum #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum dynamics #Quantum mechanics #Statistical physics

paper · doi:10.1103/physrevlett.73.1060

openalex publication_date 1994/08/22 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/29

Abstract

The reduced dynamics of a quantum system in contact with a reservoir is generally thought to be "completely positive"; this is certainly true if product initial conditions are used to define the dynamics. We show that with correlated initial conditions it need not be so. In this case the dynamics can properly be defined only on a subset of initial system states; extension, by linearity, to all possible initial states is trivially possible, but the extension may not be physically realizable and may not even be positive, let alone completely positive.

Cited by

• Solutions of generic bilinear master equations for a quantum oscillator—Positive and factorized conditions on stationary states
• The Trace Distance and Linear Entropy of Qubit States: The Role of Initial Qubit-Environment Correlations
• Lindbladian approximation beyond ultraweak coupling
• Quantum initial condition sampling for linearized density matrix dynamics: Vibrational pure dephasing of iodine in krypton matrices
• Equilibration and Typicality in Quantum Processes
• Notes on the Riccati operator equation in open quantum systems
• Purity as a witness for initial system-environment correlations in open-system dynamics
• Quantum information and relativity theory
• Decay of fidelity in terms of correlation functions
• Structure of states for which each localized dynamics reduces to a localized subdynamics
• Complete Positivity on the Subsystems Level
• Reference system and not completely positive open quantum dynamics
• Repeated temperature measurements in quantum thermodynamics
• Effects of initial system-environment correlations on open-quantum-system dynamics and state preparation
• Positivity of the assignment map implies complete positivity of the reduced dynamics
• What Does the Public Want To Know? Ask Libraries.
• Complete Positivity, Markovianity, and the Quantum Data-Processing Inequality, in the Presence of Initial System-Environment Correlations
• Unified analysis of terminal-time control in classical and quantum systems
• Algorithmic independence of initial condition and dynamical law in thermodynamics and causal inference
• Fluctuation theorems from Bayesian retrodiction
• Open system dynamics from thermodynamic compatibility
• Single-shot work extraction in quantum thermodynamics revisited
• Quantum operation [wikipedia]