Instrument-based quantum resources: quantification, hierarchies and towards constructing resource theories

TL;DR

This paper develops a comprehensive framework for instrument-based quantum resource theories, defining hierarchies and measures for various resources, thus advancing the understanding of quantum instruments in operational tasks.

Contribution

It introduces and formalizes multiple instrument-based quantum resource theories, including hierarchies and quantification methods, filling a gap in existing resource theory research.

Findings

Hierarchies of instrument-based quantum resources established

Quantitative measures for these resources developed

Framework enables systematic study of quantum instruments in operational tasks

Abstract

Quantum resources are certain features of the quantum world that provide advantages in certain information-theoretic, thermodynamic, or any other useful operational tasks that are outside the realm of what classical theories can achieve. Quantum resource theories provide us with an elegant framework for studying these resources quantitatively and rigorously. While numerous state-based quantum resource theories have already been investigated, and to some extent, measurement-based resource theories have also been explored, instrument-based resource theories remain largely unexplored, with only a few notable exceptions. As quantum instruments are devices that provide both the classical outcomes of induced measurements and the post-measurement quantum states, they are quite important, especially for scenarios where multiple parties sequentially act on a quantum system. In this work, we study several instrument-based resource theories, namely (1) the resource theory of information preservability, (2) the resource theory of (strong) entanglement preservability, (3) the resource theory of (strong) incompatibility preservability, (4) the resource theory of traditional incompatibility, and (5) the resource theory of parallel incompatibility. Furthermore, we outline the hierarchies of these instrument-based resources and provide measures to quantify them. In short, we provide a detailed framework for several instrument-based quantum resource theories.