Detecting quantum resources in a semi-device-independent framework

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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mi>d</a:mi></a:math>, we find that for any resource theory with less than <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:msup><b:mi>d</b:mi><b:mn>2</b:mn></b:msup></b:math> 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 semidevice 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.