Almost All Quantum States Have Low Entropy Rates for Any Coupling to the Environment

TL;DR

This paper demonstrates that when the environment is large, nearly all quantum states exhibit low entropy rates regardless of the coupling, indicating that most states are effectively 'lazy' in terms of entropy change.

Contribution

It proves that for sufficiently large environments, almost all quantum states have low entropy rates for any system-environment coupling.

Findings

Most states are 'pretty lazy' with low entropy rates.

Large environments lead to high prevalence of low entropy rate states.

Contrasts previous beliefs about the rarity of lazy states.

Abstract

The joint state of a system that is in contact with an environment is called lazy, if the entropy rate of the system under any coupling to the environment is zero. Necessary and sufficient conditions have recently been established for a state to be lazy [ Phys. Rev. Lett. 106 050403 (2011)], and it was shown that almost all states of the system and the environment do not have this property [ Phys. Rev. A 81 052318 (2010)]. At first glance, this may lead us to believe that low entropy rates themselves form an exception, in the sense that most states are far from being lazy and have high entropy rates. Here, we show that in fact the opposite is true if the environment is sufficiently large. Almost all states of the system and the environment are pretty lazy-their entropy rates are low for any coupling to the environment.