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

César A. Rodríguez-Rosario, Gen Kimura, Hideki Imai, and Alán Aspuru-Guzik

Phys. Rev. Lett. 106, 050403 – Published 2 February 2011

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.

Received 4 May 2010

DOI:https://doi.org/10.1103/PhysRevLett.106.050403

Authors & Affiliations

César A. Rodríguez-Rosario^1,*, Gen Kimura^2,3,†, Hideki Imai^2,3, and Alán Aspuru-Guzik^1,‡

¹Department of Chemistry and Chemical Biology, Harvard University, Cambridge, Massachusetts 02138, USA
²Research Center for Information Security (RCIS), National Institute of Advanced Industrial Science and Technology (AIST), Daibiru building 1003, 1-18-13 Sotokanda, Chiyoda-ku, Tokyo, 101-0021, Japan
³Graduate School of Science and Engineering, Chuo University, 1-13-27 Kasuga, Bunkyo-ku, Tokyo 112-8551, Japan