Thermodynamics of quantum switch information capacity activation

TL;DR

This paper investigates how quantum superpositions of causal order, via the quantum switch, can increase information capacity without violating thermodynamic laws, highlighting the role of coherence as a resource.

Contribution

It demonstrates that information capacity can increase in thermodynamic processes with indefinite causal order, constrained by resource consumption and thermodynamic laws.

Findings

Capacity increase is compatible with thermodynamics.

Only bounded capacity increases are possible.

Free energy of coherence is consumed during the process.

Abstract

We address a new setting where the second law is under question: thermalizations in a quantum superposition of causal orders, enacted by the so-called quantum switch. This superposition has been shown to be associated with an increase in the communication capacity of the channels, yielding an apparent violation of the data-processing inequality and a possibility to separate hot from cold. We analyze the thermodynamics of this information capacity increasing process. We show how the information capacity increase is compatible with thermodynamics. We show that there may indeed be an information capacity increase for consecutive thermalizations obeying the first and second laws of thermodynamics if these are placed in an indefinite order and moreover that only a significantly bounded increase is possible. The increase comes at the cost of consuming a thermodynamic resource, the free energy of coherence associated with the switch.