Joint-measurability and quantum communication with untrusted devices
arxiv(2024)
Abstract
Photon loss represents a major challenge for the implementation of quantum
communication protocols with untrusted devices, e.g. in the device-independent
(DI) or semi-DI approaches. Determining critical loss thresholds is usually
done in case-by-case studies. In the present work, we develop a general
framework for characterizing the admissible levels of loss and noise in a wide
range of scenarios and protocols with untrusted measurement devices. In
particular, we present general bounds that apply to prepare-and-measure
protocols for the semi-DI approach, as well as to Bell tests for DI protocols.
A key step in our work is to establish a general connection between quantum
protocols with untrusted measurement devices and the fundamental notions of
channel extendibility and joint-measurability, which capture essential aspects
of the communication and measurement of quantum information. In particular,
this leads us to introduce the notion of partial joint-measurability, which
naturally arises within quantum cryptography.
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