Universal Limitations on Quantum Key Distribution over a Network

Abstract

We consider the distribution of secret keys, both in a bipartite and a multipartite (conference) setting, via a quantum network and establish a framework to obtain bounds on the achievable rates. We show that any multipartite private state--the output of a protocol distilling secret key among the trusted parties--has to be genuinely multipartite entangled. In order to describe general network settings, we introduce a multiplex quantum channel, which links an arbitrary number of parties, where each party can take the role of sender only, receiver only, or both sender and receiver. We define asymptotic and non-asymptotic LOCC-assisted secret-key-agreement (SKA) capacities for multiplex quantum channels and provide strong and weak converse bounds. The structure of the protocols we consider, manifested by an adaptive strategy of secret key and entanglement [Greenberger-Horne-Zeilinger (GHZ state)] distillation over an arbitrary multiplex quantum channel, is generic. As a result, our approach also allows us to study the performance of quantum key repeaters and measurement-device-independent quantum key distribution (MDI-QKD) setups. For teleportation-covariant multiplex quantum channels, we get upper bounds on the SKA capacities in terms of the entanglement measures of their Choi states. We also obtain bounds on the rates at which secret key and GHZ states can be distilled from a finite number of copies of an arbitrary multipartite quantum state. We are able to determine the capacities for MDI-QKD setups and rates of GHZ-state distillation for some cases of interest.

Published version. Extended discussion on applicability to realistic setups of MDI-QKD

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• Experimental Quantum Communication Overcomes the Rate-loss Limit without Global Phase Tracking
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• Quantum Network: Security Assessment and Key Management
• Breaking Rate-Distance Limitation of Measurement-Device-Independent Quantum Secret Sharing
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• Secure Anonymous Conferencing in Quantum Networks
• Genuine multipartite entanglement of quantum states in the multiple-copy scenario
• Finite-key Analysis for Quantum Conference Key Agreement with Asymmetric Channels
• Speed limits on correlations in bipartite quantum systems
• Scalable High-Rate Twin-Field Quantum Key Distribution Networks without Constraint of Probability and Intensity
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• Upper bounds on device-independent quantum key distribution rates in static and dynamic scenarios
• Attainability and lower semi-continuity of the relative entropy of entanglement, and variations on the theme
• When is a Genuine Multipartite Entanglement Measure Monogamous?
• Testing of quantum nonlocal correlations under constrained free will and imperfect detectors
• Generation and evaluation of multipartite entanglement with multi-rail encoding in linear optics networks