Fundamental quantum communication tasks are linked to the ability to preserve the resourcefulness of states: Quantitative bridges are built, providing a dynamical counterpart of the Landauer's Principle.
Energy transfer and information transmission are two fundamental aspects of nature. They are seemingly unrelated, while recent findings suggest that a deep connection between them is to be discovered. This amounts to asking: Can we phrase the processes of transmitting classical bits equivalently as specific energy-transmitting tasks, thereby uncovering foundational links between them? We answer this question positively by showing that, for a broad class of classical communication tasks, a quantum dynamics' ability to transmit n bits of classical information is equivalent to its ability to transmit n units of energy in a thermodynamic task. This finding not only provides an analytical correspondence between information transmission and energy extraction tasks, but also quantifies classical communication by thermodynamics. Furthermore, our findings uncover the dynamical version of Landauer's principle, showing the strong link between transmitting information and energy. In the asymptotic regime, our results further provide thermodynamic meanings for the well-known Holevo-Schumacher-Westmoreland theorem in quantum communication theory.
The uncertainty principle is one of quantum theory's most foundational features. It underpins a quantum phenomenon called measurement incompatibility—two physical observables of a single quantum system may not always be measured simultaneously. Apart from being fundamentally important, measurement incompatibility is also a powerful resource in the broad quantum science and technologies, with wide applications to cryptography, communication, random number generation, and device-independent tasks. Since every physical system is unavoidably subject to noise, an important, yet still open, question is how to characterize the ability of noisy quantum dynamics to preserve measurement incompatibility. This work fills this gap by providing a resource theory of this ability, termed incompatibility preservability. We quantify incompatibility preservability by a robustness measure. Then, we introduce an operational task, entanglement-assisted filter game, to completely characterize both the robustness measure and the conversion of incompatibility preservability. Our results provide a general framework to describe how noisy dynamics affect the uncertainty principle's signature.
Information is instrumental in our understanding of thermodynamics. Their interplay has been studied through completely degenerate Hamiltonians whereby the informational contributions to thermodynamic transformations can be isolated. In this setting, all states other than the maximally mixed state are considered to be in informational nonequilibrium. An important yet still open question is how to characterize the ability of quantum dynamics to preserve informational nonequilibrium. Here, the dynamical resource theory of informational nonequilibrium preservability is introduced to begin providing an answer to this question. A characterization of the allowed operations is given for qubit channels and the n-dimensional Weyl-covariant channels-a physically relevant subset of the general channels. An operational interpretation of a state discrimination game with Bell state measurements is given. Finally, an explicit link between a channel's classical capacity and its ability to preserve informational nonequilibrium is made.