Fundamental Limits of Repeaterless Quantum Communications

Stefano Pirandola, Riccardo Laurenza, Carlo Ottaviani, Leonardo Banchi

Research output: Working paperPreprint


Quantum communications promises reliable transmission of quantum information, efficient distribution of entanglement and generation of completely secure keys. For all these tasks there is a crucial question to answer: What are their optimal rates without quantum repeaters? Our work solves this basic question for any two parties connected by a quantum channel, without any restriction on their classical communication, which can be unlimited and two-way. We design a method which reduces the most general protocol of quantum communication to the computation of a novel quantity, identified as the channel's relative entropy of entanglement. In this way, we bound the ultimate rates that are achievable over the most important bosonic and qubit channels, computing a number of exact formulas for their two-way capacities. In particular, we determine the fundamental rate-loss scaling which affects any quantum optical communication. By setting these limits, we establish the most general and correct benchmarks for testing the performance of quantum repeaters.
Original languageEnglish
Number of pages34
Publication statusPublished - 29 Oct 2015


  • quant-ph

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