Fundamental rate-loss tradeoff for optical quantum key distribution

TL;DR

This paper establishes a fundamental limit on the secret key rate for optical quantum key distribution over lossy channels, indicating that surpassing this rate-distance tradeoff without quantum repeaters is impossible.

Contribution

It proves an upper bound on the secret-key-agreement capacity of lossy optical channels, highlighting the necessity of quantum repeaters for high-rate long-distance QKD.

Findings

Secret-key capacity limited by channel loss

No protocol can exceed the derived upper bound

Quantum repeaters are essential for high-rate long-distance QKD

Abstract

Since 1984, various optical quantum key distribution (QKD) protocols have been proposed and examined. In all of them, the rate of secret key generation decays exponentially with distance. A natural and fundamental question is then whether there are yet-to-be discovered optical QKD protocols (without quantum repeaters) that could circumvent this rate-distance tradeoff. This paper provides a major step towards answering this question. We show that the secret-key-agreement capacity of a lossy and noisy optical channel assisted by unlimited two-way public classical communication is limited by an upper bound that is solely a function of the channel loss, regardless of how much optical power the protocol may use. Our result has major implications for understanding the secret-key-agreement capacity of optical channels---a long-standing open problem in optical quantum information theory---and strongly suggests a real need for quantum repeaters to perform QKD at high rates over long distances.