Measurement-device-independent resource characterization protocols

Abstract: Measurement-device-independent (MDI) quantum information processing tasks are important subroutines in quantum information science because they are robust against any type of measurement imperfections. In this work, we propose a framework of MDI resource characterization protocols that unifies and generalizes these tasks. We show that resources that do not increase under local operation and shared randomness can be characterized with any untrusted measurement, and we provide a general procedure to convert such resource characterization tasks into MDI protocols. We then focus on applying our framework to two cases that satisfy the criteria: the resource theory of bipartite and multipartite entanglement, and the resource theory of quantum memories. We demonstrate several MDI characterization protocols for these resources. These protocols are either novel or generalize existing ones from the literature. We also show that MDI quantum key distribution can be viewed as an MDI quantification protocol for quantum memory.