Quantum measurements constrained by the third law of thermodynamics

TL;DR

This paper explores how the third law of thermodynamics limits the ability to perform ideal quantum measurements, showing that certain measurement properties are impossible for sharp observables but may be feasible for unsharp ones.

Contribution

It introduces an operational formulation of the third law for quantum transformations and analyzes its implications for the properties of general quantum measurements.

Findings

Ideal projective measurements are ruled out by the third law.

Some measurement properties can be achieved with unsharp observables.

The third law constrains the sharpness of quantum measurements.

Abstract

In the quantum regime, the third law of thermodynamics implies the unattainability of pure states. As shown recently, such unattainability implies that a unitary interaction between the measured system and a measuring apparatus can never implement an ideal projective measurement. In this paper, we introduce an operational formulation of the third law for the most general class of physical transformations, the violation of which is both necessary and sufficient for the preparation of pure states. Subsequently, we investigate how such a law constrains measurements of general observables, or positive operator valued measures. We identify several desirable properties of measurements which are simultaneously enjoyed by ideal projective measurements -- and are hence all ruled out by the third law in such a case -- and determine if the third law allows for these properties to obtain for general measurements of general observables and, if so, under what conditions. It is shown that while the third law rules out some of these properties for all observables, others may be enjoyed by observables that are sufficiently "unsharp".