A hierarchy of thermodynamically consistent quantum operations

TL;DR

This paper develops a hierarchy of quantum operations and measurements consistent with thermodynamic laws, clarifying which quantum processes are thermodynamically feasible and how thermodynamics constrains quantum measurements.

Contribution

It introduces a hierarchy of thermodynamically consistent quantum operations and characterizes their properties, linking thermodynamic principles to quantum process constraints.

Findings

Channels in the hierarchy are characterized by positivity and rank properties.

Thermodynamics restricts the realizability of certain quantum measurements.

Operations consistent with the third law must not perturb strictly positive states.

Abstract

In order to determine what quantum operations and measurements are consistent with the laws of thermodynamics, one must start by allowing all processes allowed by the framework of quantum theory, and then impose the laws of thermodynamics as a set of constraints. Here, we consider a hierarchy of quantum operations and measurements that are consistent with ($I$) the weak third law, ($II$) the strong third law, and ($III$) both the second and the third laws of thermodynamics, i.e., operations and measurements that are fully consistent with thermodynamics. Such characterisation allows us to identify which particular thermodynamic principle is responsible for the (un)attainability of a given quantum operation or measurement. In the case of channels, i.e., trace-preserving operations, we show that a channel belongs to ($I$) and ($II$) if and only if it is strictly positive and rank non-decreasing, respectively, whereas a channel belongs to ($III$) only if it is rank non-decreasing and does not perturb a strictly positive state. On the other hand, while thermodynamics does not preclude the measurability of any POVM, the realisable state-update rules for measurements are increasingly restricted as we go from ($I$) to ($III$).