The nonequilibrium cost of accurate information processing

TL;DR

This paper derives a fundamental, computable limit on the accuracy of information processing systems based on their nonequilibrium resources, applicable to quantum and classical systems, with implications for device efficiency and quantum advantages.

Contribution

It introduces the concept of reverse entropy to quantify nonequilibrium resources and establishes a universal limit on information processing accuracy under quantum laws.

Findings

The limit applies to all deterministic classical computations and quantum extensions.

Optimal tradeoffs between nonequilibrium resources and accuracy are characterized for key information tasks.

Framework demonstrates potential thermodynamical advantages of quantum devices.

Abstract

Accurate information processing is crucial both in technology and in nature. To achieve it, any information processing system needs an initial supply of resources away from thermal equilibrium. Here we establish a fundamental limit on the accuracy achievable with a given amount of nonequilibrium resources. The limit applies to arbitrary information processing tasks and arbitrary information processing systems subject to the laws of quantum mechanics. It is easily computable and is expressed in terms of an entropic quantity, which we name reverse entropy, associated to a time reversal of the information processing task under consideration. The limit is achievable for all deterministic classical computations and for all their quantum extensions. As an application, we establish the optimal tradeoff between nonequilibrium and accuracy for the fundamental tasks of storing, transmitting, cloning, and erasing information. Our results set a target for the design of new devices approaching the ultimate efficiency limit, and provide a framework for demonstrating thermodynamical advantages of quantum devices over their classical counterparts.