Abstract
Irreversibility, crucial in both thermodynamics and information theory, is naturally studied by comparing the evolution—the (forward) channel—with an associated reverse—the reverse channel. There are two natural ways to define this reverse channel. Using logical inference, the reverse channel is the Bayesian retrodiction (the Petz recovery map in the quantum formalism) of the original one. Alternatively, we know from physics that every irreversible process can be modeled as an open system: one can then define the corresponding closed system by adding a bath (“dilation”), trivially reverse the global reversible process, and finally remove the bath again. We prove that the two recipes are strictly identical, both in the classical and in the quantum formalism, once one accounts for correlations formed between system and the bath. Having established this, we define and study special classes of maps: product-preserving maps (including generalized thermal maps), for which no such system-bath correlations are formed for some states; and tabletop time-reversible maps, when the reverse channel can be implemented with the same devices as the original one. We establish several general results connecting these classes, and a very detailed characterization when both the system and the bath are one qubit. In particular, we show that, when reverse channels are well defined, product preservation is a sufficient but not necessary condition for tabletop reversibility; and that the preservation of local energy spectra is a necessary and sufficient condition to generalized thermal operations.
- Received 10 October 2023
- Accepted 29 January 2024
DOI:https://doi.org/10.1103/PRXQuantum.5.010332
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.
Published by the American Physical Society
Physics Subject Headings (PhySH)
Popular Summary
From the scrambling of an egg, to corruption of a file, all the way to ageing, irreversibility is everywhere. Yet in physics, the reverse process is not always straightforward to come up with. There seems to be two main ways to go about it. We could use the famous Bayes’ rule to invert the process in a logically consistent way, or we could understand the irreversible process as simply being part of a “bigger” reversible process that we do not know the details about (and thus, we simply think it is irreversible because of our ignorance).
In this work, we show that these two ways are actually the same thing (even when the process is totally quantum) as long as we keep track of the correlations that form because of the bigger reversible process. We also explore questions surrounding when these are the same even when we fail to keep track of these correlations—which can be seen as corresponding to times where the reverse process and the forward process “use the same devices” or “tabletop” (hence, the term tabletop reversibility). All of this gives insights into the nature of reversibility and reversal as a whole, even in the quantum regime.
