Thermodynamic criteria for signaling in quantum channels

Signaling quantum channels are fundamental to quantum communication, enabling the transfer of information from input to output states. In contrast, thermalization erases information about the initial state. This raises a crucial question: How does the thermalizing 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. Analyzing 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.