Joint-measurability and quantum communication with untrusted devices

TL;DR

This paper introduces a comprehensive framework for assessing loss and noise thresholds in quantum communication protocols with untrusted devices, linking these thresholds to fundamental quantum measurement concepts.

Contribution

It develops a general method to determine loss and noise limits in various untrusted quantum protocols, connecting them to channel extendibility and joint-measurability.

Findings

Established bounds for semi-DI and DI protocols.

Linked loss thresholds to channel extendibility.

Introduced the concept of partial joint-measurability.

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.