Linear programs for entanglement and key distribution in the quantum internet

Abstract

Quantum networks will allow to implement communication tasks beyond the reach of their classical counterparts. A pressing and necessary issue for the design of quantum network protocols is the quantification of the rates at which these tasks can be performed. Here, we propose a simple recipe that yields efficiently computable lower and upper bounds on the maximum achievable rates. For this we make use of the max-flow min-cut theorem and its generalization to multi-commodity flows to obtain linear programs. We exemplify our recipe deriving the linear programs for bipartite settings, settings where multiple pairs of users obtain entanglement in parallel as well as multipartite settings, covering almost all known situations. We also make use of a generalization of the concept of paths between user pairs in a network to Steiner trees spanning a group of users wishing to establish Greenberger-Horne-Zeilinger states.

arXiv comment37 pages, 10 figures. Published version

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• Quantum repeaters: From quantum networks to the quantum internet
• Entanglement Distribution in a Quantum Network, a Multi-Commodity Flow-Based Approach
• Tools for quantum network design
• Universal Limitations on Quantum Key Distribution over a Network
• Distributing Multipartite Entanglement over Noisy Quantum Networks
• Statistical properties of the quantum internet
• Multi-User Entanglement Distribution in Quantum Networks Using Multipath Routing
• Fast and reliable entanglement distribution with quantum repeaters: principles for improving protocols using reinforcement learning
• On the design and analysis of near-term quantum network protocols using Markov decision processes
• On the Bipartite Entanglement Capacity of Quantum Networks
• Reducing classical communication costs in multiplexed quantum repeaters using hardware-aware quasi-local policies
• Asymmetric quantum multicast network coding: asymmetric optimal cloning over quantum networks
• Disti-Mator: an entanglement distillation-based state estimator
• Fidelity-Aware Multipath Routing for Multipartite State Distribution in Quantum Networks
• Quantum Max-Flow Min-Cut theorem
• Multicast quantum network coding as optimal symmetric universal cloning over a quantum network
• Spanning-tree-packing protocol for conference key propagation in quantum networks