Sufficient and Necessary Condition for Zero Quantum Entropy Rates under any Coupling to the Environment

2010/04/30 by César A. Rodríguez-Rosario, Cesar A. Rodriguez-Rosario, Gen Kimura +3 · 2 citations
Computer Science · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Quantum Information and Cryptography #Quantum Mechanics and Applications #math-ph #math.MP #quant-ph

paper · pdf · doi:10.1103/physrevlett.106.050403

published as Phys. Rev. Lett. 106, 050403 (2011) · 4 pages

arxiv created 2011/01/18 · openalex publication_date 2011/02/02 · arxiv updated 2011/02/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We find the necessary and sufficient conditions for the entropy rate of the system to be zero under any system-environment Hamiltonian interaction. We call the class of system-environment states that satisfy this condition lazy states. They are a generalization of classically correlated states defined by quantum discord, but based on projective measurements of any rank. The concept of lazy states permits the construction of a protocol for detecting global quantum correlations using only local dynamical information. We show how quantum correlations to the environment provide bounds to the entropy rate, and how to estimate dissipation rates for general non-Markovian open quantum systems.

Citations

• Entanglement Capabilities of Nonlocal Hamiltonians
• Completely positive maps and classical correlations
• Completely positive dynamical semigroups of N-level systems
• Decoherence, einselection, and the quantum origins of the classical
• Classical, quantum and total correlations
• Linear assignment maps for correlated system-environment states

Cited by

• Which Bipartite States are Lazy
• Unifying Treatment of Discord via Relative Entropy