Accessible bounds for general quantum resources

TL;DR

This paper introduces a general framework to efficiently estimate lower bounds of quantum resource measures by projecting states onto a restricted subset, simplifying calculations and reducing experimental effort.

Contribution

It provides a universal method to obtain lower bounds for any quantum resource quantifier satisfying monotonicity, applicable across various quantum resources.

Findings

Framework yields quantitative lower bounds for quantum resources.

Reduces computational and experimental complexity.

Applicable to multiqubit entanglement and other resources.

Abstract

The recent development of general quantum resource theories has given a sound basis for the quantification of useful quantum effects. Nevertheless, the evaluation of a resource measure can be highly non-trivial, involving an optimisation that is often intractable analytically or intensive numerically. In this paper, we describe a general framework that provides quantitative lower bounds to any resource quantifier that satisfies the essential property of monotonicity under the corresponding set of free operations. Our framework relies on projecting all quantum states onto a restricted subset using a fixed resource non-increasing operation. The resources of the resultant family can then be evaluated using a simplified optimisation, with the result providing lower bounds on the resource contents of any state. This approach also reduces the experimental overhead, requiring only the relevant statistics of the restricted family of states. We illustrate the application of our framework by focusing on the resource of multiqubit entanglement and outline applications to other quantum resources.