Operational quantification of continuous-variable quantum resources

The diverse range of resources which underlie the utility of quantum states in practical tasks motivates the development of universally applicable methods to measure and compare resources of different types. However, many of such approaches were hitherto limited to the finite-dimensional setting or were not connected with operational tasks. We overcome this by introducing a general method of quantifying resources for continuous-variable quantum systems based on the robustness measure, applicable to a plethora of physically relevant resources such as optical nonclassicality, entanglement, genuine non-Gaussianity, and coherence. We demonstrate in particular that the measure has a direct operational interpretation as the advantage enabled by a given state in a class of channel discrimination tasks. We show that the robustness constitutes a well-behaved, bona fide resource quantifier in any convex resource theory, contrary to a related negativity-based measure known as the standard robustness. Furthermore, we show the robustness to be directly observable-it can be computed as the expectation value of a single witness operator-and establish general methods for evaluating the measure. Explicitly applying our results to the relevant resources, we demonstrate the exact computability of the robustness for several classes of states.Ministry of Education (MOE)Nanyang Technological UniversityNational Research Foundation (NRF)Published versionB. R. is supported by the Presidential Postdoctoral Fellowship from Nanyang Technological University, Singapore. L. L. is supported by the ERC Synergy Grant BIOQ (Grant No. 319130) and by the Alexander von Humboldt Foundation. G. F. acknowledges the support received from the EU through the ERASMUS þ Traineeship program and from the Scuola Galileiana di Studi Superiori. R. T. acknowledges the support of NSF, ARO, IARPA, AFOSR, the Takenaka Scholarship Foundation, and the National Research Foundation (NRF) Singapore, under its NRFF Fellow programme (Grant No. NRF-NRFF2016-02) and the Singapore Ministry of Education Tier 1 Grant No. 2019-T1-002-015. Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not reflect the views of National Research Foundation, Singapore