Inferring general links between energetics and information with unknown environment

Identifying general links between energetics and information in realistic open quantum systems is a long-standing problem in quantum thermodynamics and quantum information processing. However, the generality of existing efforts is often impeded by their specific assumptions about environments. Here we address the problem by developing a trajectory-level thermodynamic inference theory to establish general links using just the knowledge of the system, enabling a single framework applicable to a diverse range of environments. Underpinning the framework is a notion of excess energy introduced for inferring the net energy gain of the system after completing an information processing trajectory. We show that fluctuation behaviors of the excess energy encode general links between energetics and information with a conceptual advantage that they completely avoid assumptions about environments and system-environment coupling forms. Crucially, we obtain a single thermodynamic inequality that integrates upper bounds on heat dissipation and extracted work in terms of system's information content change, providing complementary constraints that greatly expand the context of existing well-adopted results based on the second law of thermodynamics. We also uncover lower bounds on the precision of the fluctuating system's energy and information content changes in terms of their Fano factors and a correlation function between them. By extending relations between energetics and information to higher-order fluctuations, we thus reveal a trade-off that a more precise inference of energy or information content changes requires a looser energetic-information link. We showcase the implications of these general links in a number of quantum information and thermodynamic tasks of application relevance. Our framework provides a toolkit for analyzing the interplay between energetics and information from the trajectory level in generic quantum systems, thereby adding an indispensable structure to the thermodynamics of information. Published by the American Physical Society 2024