Thermodynamic criteria for signaling in quantum channels

TL;DR

This paper explores the fundamental relationship between the signaling capacity of quantum channels and their thermodynamic properties related to athermality, establishing bounds and trade-offs crucial for quantum communication.

Contribution

It introduces measures for athermality generation, preservation, and transmission, and links these to the signaling capabilities of quantum channels, revealing fundamental thermodynamic constraints.

Findings

Signaling ability is upper-bounded by athermality preservation.

Signaling ability is lower-bounded by athermality transmission.

Trade-off demonstrated in the quantum switch example.

Abstract

Signaling quantum channels are fundamental to quantum communication, enabling the transfer of information from input to output states. In contrast, thermalisation erases information about the initial state. This raises a crucial question: How does the thermalising tendency of a quantum channel constrain its signaling power and vice versa? In this work, we address this question by considering three thermodynamic tasks associated with a quantum channel: the generation, preservation, and transmission of athermality. We provide faithful measures for athermality generation and athermality preservation of quantum channels, and prove that their difference quantifies athermality transmission. Analysing these thermodynamic tasks, we find that the signaling ability of a quantum channel is upper-bounded by its athermality preservation and lower-bounded by its athermality transmission, thereby establishing a fundamental relationship between signaling and thermodynamic properties of channels for quantum communication. We demonstrate this interplay for the example of the quantum switch, revealing an explicit trade-off between the signaling ability and athermality of the quantum channels it can implement.