Detecting quantum resources in a semi-device independent framework

TL;DR

This paper develops a semi-device independent framework to detect quantum resources in prepare-and-measure scenarios, providing explicit witnesses and conditions for resource detection based on the dimension and the structure of free states or operations.

Contribution

It introduces a novel semi-device independent method for detecting quantum resources and constructs explicit witnesses for various resources in a dimension-restricted setting.

Findings

Existence of correlations that detect quantum resources for certain resource theories.

Framework applicable for any dimension with fewer than d^2 free states or operations.

Explicit construction of witnesses for various quantum resources.

Abstract

We investigate whether one can detect the presence of a quantum resource in some operational task or equivalently whether every quantum resource provides an advantage over its free counterpart in some black box scenarios where one does not have much information about the devices. For any dimension $d$, we find that for any resource theory with less than $d^2$ number of linearly independent free states or free operations, there exist correlations that can detect the presence of a quantum resource. For this purpose, we introduce the framework for detecting quantum resources semi-device independently by considering the prepare-and-measure scenario with the restriction on the dimension of the quantum channel connecting the preparation box with the measurement box. We then explicitly construct witnesses to observe the presence of various quantum resources. We expect these results will open avenues for detecting and finding uses of quantum resources in general operational tasks.