Quantum Reference Frames and Their Applications to Thermodynamics

TL;DR

This paper introduces a practical quantum reference frame that enables approximate unitary operations respecting conservation laws, acting as a battery and facilitating thermodynamic processes with multiple conserved quantities.

Contribution

It presents a physically intuitive, implementable quantum reference frame construction that handles multiple conserved quantities, including non-commuting ones, with finite resources.

Findings

Constructed a finite, implementation-friendly quantum reference frame.

Demonstrated the frame's ability to implement unitaries respecting conservation laws.

Applied the framework to quantum thermodynamics with multiple conserved quantities.

Abstract

We construct a quantum reference frame, which can be used to approximately implement arbitrary unitary transformations on a system in the presence of any number of extensive conserved quantities, by absorbing any back action provided by the conservation laws. Thus, the reference frame at the same time acts as a battery for the conserved quantities. Our construction features a physically intuitive, clear and implementation-friendly realisation. Indeed, the reference system is composed of the same types of subsystems as the original system and is finite for any desired accuracy. In addition, the interaction with the reference frame can be broken down into two-body terms coupling the system to one of the reference frame subsystems at a time. We apply this construction to quantum thermodynamic setups with multiple, possibly non-commuting conserved quantities, which allows for the definition of explicit batteries in such cases.