Quantifying memory capacity as a quantum thermodynamic resource

TL;DR

This paper introduces a formalism to quantify the thermodynamic value of quantum memory, called thermal information capacity, which converges to non-equilibrium Helmholtz free energy and is computed explicitly for qubits.

Contribution

It develops a general framework for quantifying quantum memory's thermodynamic value and computes the capacity exactly for qubits away from the thermodynamic limit.

Findings

Thermal information capacity converges to non-equilibrium Helmholtz free energy.

Exact capacity computed for two-state quantum memories.

Memory-bath coupling can approximate optimal capacity arbitrarily well.

Abstract

The information-carrying capacity of a memory is known to be a thermodynamic resource facilitating the conversion of heat to work. Szilard's engine explicates this connection through a toy example involving an energy-degenerate two-state memory. We devise a formalism to quantify the thermodynamic value of memory in general quantum systems with nontrivial energy landscapes. Calling this the thermal information capacity, we show that it converges to the non-equilibrium Helmholtz free energy in the thermodynamic limit. We compute the capacity exactly for a general two-state (qubit) memory away from the thermodynamic limit, and find it to be distinct from known free energies. We outline an explicit memory--bath coupling that can approximate the optimal qubit thermal information capacity arbitrarily well.