The resource theory of interactive quantum instruments

TL;DR

This paper develops a resource theory for quantum instruments, quantifying their ability to interact coherently with quantum states and linking this to operational tasks like entanglement preservation.

Contribution

It introduces a resource quantifier for interactive quantum instruments, with three operational interpretations, and unifies existing resource theories for channels and measurements.

Findings

The resource quantifier admits three operational interpretations.

The ability to recover classical information fully characterizes the resource.

The framework generalizes existing resource theories for channels and measurements.

Abstract

Quantum instruments describe both the classical output and the updated quantum state in a measurement process. To do this in a non-trivial way, instruments must have the capability to interact coherently with the state that they measure. Here, we develop a resource theory for instruments. We consider a relevant quantifier of the separation between interactive and non-interactive instruments and show that it admits three distinct operational interpretations in terms of quantum information tasks. These concern (i) the preservation of maximally entangled states after a local measurement, (ii) the average ability to preserve random states after measurement, and (iii) the ability to recover the classical information generated from measuring half of a maximally entangled state. We also introduce a natural set of allowed operations and show that the third task fully characterises the resource content of instruments. Our general framework reproduces as special cases established resource theories for channels and measurements.