The Resource Theory of Quantum States Out of Thermal Equilibrium (1111.3882v3)

Abstract: The ideas of thermodynamics have proved fruitful in the setting of quantum information theory, in particular the notion that when the allowed transformations of a system are restricted, certain states of the system become useful resources with which one can prepare previously inaccessible states. The theory of entanglement is perhaps the best-known and most well-understood resource theory in this sense. Here we return to the basic questions of thermodynamics using the formalism of resource theories developed in quantum information theory and show that the free energy of thermodynamics emerges naturally from the resource theory of energy-preserving transformations. Specifically, the free energy quantifies the amount of useful work which can be extracted from asymptotically-many copies of a quantum system when using only reversible energy-preserving transformations and a thermal bath at fixed temperature. The free energy also quantifies the rate at which resource states can be reversibly interconverted asymptotically, provided that a sublinear amount of coherent superposition over energy levels is available, a situation analogous to the sublinear amount of classical communication required for entanglement dilution.

• The paper introduces a resource-theoretic framework that uses free energy to quantify the work extractable from athermal quantum states.
• It employs energy-preserving operations and thermal state preparations to establish state interconvertibility and gauge resourcefulness.
• The findings bridge quantum information theory and thermodynamics, offering insights applicable to quantum engines and refrigeration cycles.

The Resource Theory of Quantum States Out of Thermal Equilibrium

The integration of thermodynamic concepts into quantum information theory has provided a robust framework for understanding quantum states as resources when subjected to constraints. The paper "The Resource Theory of Quantum States Out of Thermal Equilibrium" by Brandão, Horodecki, Oppenheim, Renes, and Spekkens explores this framework, assessing quantum states' capacity to yield useful work under defined energy-preserving transformations.

Quantum Resource Theories and Thermal Operations

Quantum resource theories conceptualize quantum operations under particular restrictions, delineating states outside a set as resources permitting otherwise inaccessible operations. This paper utilizes the recent advancements in quantum resource theories to address thermodynamic phenomena by restricting operations to energy-conserving unitaries and the preparation of any ancillary systems in a thermal state at temperature $T$. This restriction elucidates the operational nature of athermal states, those not in thermal equilibrium at temperature $T$, as resources.

Free Energy as a Measure of Resourcefulness

The central innovation of this paper is refining the notion of free energy within the framework of quantum resource theories. It is shown that the conventional thermodynamic free energy quantifies the maximum work extractable from quantum systems when subjected to energy-preserving transformations in the presence of a thermal bath. Crucially, the free energy determines not only the extractable work but also the interconvertibility rate of quantum states given access to a thermal reservoir, effectively quantifying the resourcefulness of quantum states out of equilibrium.

Theoretical Implications and Practical Applications

Several implications can be drawn from this research. Theoretically, using the entropy relative to a thermal Gibbs state as a resource measure establishes a more profound connection between quantum information theory and statistical mechanics. The paper extends existing understanding by showing that states' interconvertibility and resource utility can be precisely calculated, opening avenues for new conservation laws and transition conditions in quantum thermodynamics.

Practically, this framework potentially impacts areas like quantum computing and quantum thermodynamic systems design, offering a rigorous method to evaluate the utility of quantum states in energy-controlled environments. Further developments may enable more efficient quantum engines and refrigeration cycles, harnessing the potential of quantum coherence and athermality.

Conclusion and Future Directions

The framework and results presented provide a fertile ground for future explorations in quantum thermodynamics. The formal establishment of free energy as the pivotal measure in the reversible interconversion of quantum states could catalyze advances in studying quantum engines and other nonequilibrium systems. Subsequent research may extend these results to broader classes of operations and diverse temperature regimes, refining both theoretical constructs and practical methodologies in quantum technologies.