An operational characterization of infinite-dimensional quantum resources

TL;DR

This paper develops a method to extend finite-dimensional quantum resource characterizations to infinite-dimensional systems, providing an operational interpretation for continuous variable quantum resources via quantum games.

Contribution

It introduces a technique for approximating infinite-dimensional resource measures with finite-dimensional ones, establishing conditions for tightness and applicability to continuous variable quantum resources.

Findings

The technique applies to various continuous variable quantum resources.

It provides an operational interpretation through quantum game advantages.

The approach extends the max relative entropy interpretation to infinite dimensions.

Abstract

Recently, various non-classical properties of quantum states and channels have been characterized through an advantage they provide in specific quantum information tasks over their classical counterparts. Such advantage can be typically proven to be quantitative, in that larger amounts of quantum resources lead to better performance in the corresponding tasks. So far, these characterizations have been established only in the finite-dimensional setting. In this manuscript, we present a technique for extending the known results to the infinite-dimensional regime. The technique relies on approximating infinite-dimensional resource measures by their finite-dimensional counterparts. We give a sufficient condition for the approximation procedure to be tight, i.e. to match with established infinite-dimensional resource quantifiers, and another sufficient condition for the procedure to match with relevant extensions of these quantifiers. We show that various continuous variable quantum resources fall under these conditions, hence, giving them an operational interpretation through the advantage they can provide in so-called quantum games. Finally, we extend the interpretation to the max relative entropy in the infinite-dimensional setting.