Robust certification of non-projective measurements: theory and experiment

TL;DR

This paper presents a general, scalable method to certify non-simulability of quantum measurements, demonstrated experimentally with trapped-ion qudits, advancing the understanding of measurement advantages in quantum information.

Contribution

It introduces a hierarchy of semidefinite programs for certifying non-simulability of POVMs, with experimental validation and robustness enhancements.

Findings

Successfully certified non-simulability of 2- and 3-dimensional POVMs

Developed a hierarchy of semidefinite programs for certification

Extended framework to include ancillary systems

Abstract

Determining the conditions under which positive operator-valued measures (POVMs), the most general class of quantum measurements, outperform projective measurements remains a challenging and largely unresolved problem. Of particular interest are projectively simulable POVMs, which can be realized through probabilistic mixtures of projective measurements, and therefore offer no advantage over projective schemes. Characterizing the boundary between simulable and non-simulable POVMs is, however, a difficult task, and existing tools either fail to scale efficiently, provide limited experimental feasibility or work only for specific POVMs. Here, we introduce and demonstrate a general method to certify non-simulability of a POVM by introducing a hierarchy of semidefinite programs. It provides upper bounds on the non-simulability measure of critical visibility of arbitrary POVMs which are tight in many cases and outperform previously known criteria. We experimentally certify the non-simulability of two- and three-dimensional POVMs using a trapped-ion qudit quantum processor by constructing non-simulability witnesses and introduce a modification of our framework that makes them robust against state preparation errors. Finally, we extend our results to the setting where an additional ancilla system is available.