Information Processing in Quantum Thermodynamic Systems: an Autonomous Hamiltonian Approach

TL;DR

This paper extends quantum thermodynamics to include information processing with initial correlations, deriving new constraints and bounds for autonomous systems, and linking quantum speed limits to thermodynamic and hypothesis testing principles.

Contribution

It generalizes the second law for correlated quantum systems within an autonomous Hamiltonian framework and introduces a quantum thermodynamic speed limit related to Landauer's bound.

Findings

Derived constraints on Hamiltonians ensuring catalyst behavior.

Established a quantum speed limit for thermodynamic processes.

Linked quantum speed limits to hypothesis testing.

Abstract

Extending the quantum formulation of [Phys. Rev. X 3, 041003 (2013)] to a more general setting for studying the thermodynamics of information processing including initial correlations, we generalize the second law of thermodynamics to account for information processing in such autonomous systems. We consider a composite quantum system consisting of a principal system, heat bath, memory, and work source, and adopt an autonomous Hamiltonian framework. We derive constraints on the total Hamiltonian that ensure the work source to act as a catalyst preserving its original randomness, namely that the total unitary evolution must have a unitary partial transpose. We show that this requirement is equivalent to the commutativity of operators acting on the joint system of the principal system, bath, and memory, which underlies the Hamiltonian structure. Next, we generalize the quantum speed limit for the joint dynamics of system and memory to the quantum thermodynamic speed limit, from which we obtain a dynamical version of Landauer's bound. More importantly, we also interpret this quantum thermodynamic speed limit in the context of quantum hypothesis testing.