System–Bath Reversible and Irreversible Quantum Dynamics

Clive Cenxin Aw, Lin Htoo Zaw, Maria Balanzó-Juandó +1 more

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: (including ), for which no such system-bath correlations are formed for some states; and , 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. Published by the American Physical Society 2024

Fabio Benatti, Roberto Floreanini B

Raisa I. Karasik

Sreenath K. Manikandan, Cyril Elouard, Andrew N. Jordan

Fluctuation theorems are relations constraining the out-of-equilibrium fluctuations of thermodynamic quantities like the entropy production that were initially introduced for classical or quantum systems in contact with a thermal bath. Here we show, in the absence of thermal bath, the dynamics of continuously measured quantum systems can also be described by a fluctuation theorem, expressed in terms of a recently introduced arrow of time measure. This theorem captures the emergence of irreversible behavior from microscopic reversibility in continuous quantum measurements. From this relation, we demonstrate that measurement-induced wave-function collapse exhibits absolute irreversibility, such that Jarzynski-like equalities are violated, and that this property is inherent to quantum information acquisition. We apply our results to different continuous measurement schemes on a qubit: dispersive measurement, homodyne, and heterodyne detection of qubit's fluorescence.

Blind Review

When admissible states and dynamics are restricted to pure states and reversible dynamics, the BBBV theorem largely prohibits exponential speedup of quantum search over classical search. However, the recent Chen-Huang-Preskill-Zhou (CHPZ) quantum (thermal) gradient descent proposal suggests system-heat bath interactions may offer more by leveraging irreversible dynamics. We simplify the complex CHPZ analysis by casting everything in terms of quantum equilibrium thermodynamics with some loss of generality. The key point is that different initial system temperatures arise depending on the answer of a decision problem despite sharing the same initial n-qubit system (thermal) state - infinite temperature (for the yes answer) versus the heat bath temperature (for the no answer). By tracing dynamics of either the n-qubit system or heat baths, the decision problem may be solved efficiently - quantum thermal search. Some issues with the efficiency conclusion are explored, in terms of either simulating thermal interactions with polynomially-scaling inverse bath temperature or accuracy of heat bath approximations.

Giulio Casati