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- Title
Linear programs for entanglement and key distribution in the quantum internet.
- Authors
Bäuml, Stefan; Azuma, Koji; Kato, Go; Elkouss, David
- 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. The study of a quantum network becomes particularly challenging in the presence of multiple users that simultaneously access its resources. Using linear programming techniques, this work investigates upper and lower bounds to the communication rates that are achievable by remote users in the network per total number of channel uses.
- Subjects
QUANTUM networks (Optics); LINEAR programming; BIPARTITE graphs; QUANTUM communication (Optics); QUANTUM optics
- Publication
Communications Physics, 2020, Vol 3, Issue 1, p1
- ISSN
2399-3650
- Publication type
Article
- DOI
10.1038/s42005-020-0318-2