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 nonasymptotic local quantum operations and classical communication-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.
- Received 30 September 2020
- Revised 15 July 2021
- Accepted 23 July 2021
DOI:https://doi.org/10.1103/PhysRevX.11.041016
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
Published by the American Physical Society
Physics Subject Headings (PhySH)
Popular Summary
Secure communication is at the heart of hopes for a quantum-based internet. Such a network would use principles of quantum physics to generate secret encryption keys that are, in principle, unbreakable. But many questions remain with regard to security criteria for these systems and the rate at which they can generate secure keys. Here, we present a mathematical framework for obtaining bounds on achievable rates of entanglement-based protocols.
First, we introduce the most general form of a quantum-network channel, which we refer to as a multiplex channel. We then determine fundamental limitations on secret key distribution over quantum multiplex channels against a quantum eavesdropper while using the most general adaptive strategy. According to this strategy, trusted parties are allowed to perform local operations and classical communication between channel uses.
The essential step in our multifaceted project is to show that any entanglement-based protocol used to distill cryptographic keys among many parties must employ a genuinely multipartite entangled state. Using this finding, we provide bounds on the secret key rates among an arbitrary number of trusted parties over a network. These bounds are in terms of quantities that measure the potential for entanglement generation of quantum multiplex channels.
The generic structure of our protocol and bounds allows us to also determine limitations on quantum-key repeaters and rates of measurement-device-independent quantum-key distribution. Furthermore, for certain cases of interest, we determine the maximum rates at which a secret key can be shared among trusted parties.
