The squashed entanglement of a quantum channel

Masahiro Takeoka, Saikat Guha, Mark M. Wilde

Research output: Contribution to journalArticle

54 Scopus citations

Abstract

This paper defines the squashed entanglement of a quantum channel as the maximum squashed entanglement that can be registered by a sender and receiver at the input and output of a quantum channel, respectively. A new subadditivity inequality for the original squashed entanglement measure of Christandl and Winter leads to the conclusion that the squashed entanglement of a quantum channel is an additive function of a tensor product of any two quantum channels. More importantly, this new subadditivity inequality, along with prior results of Christandl and Winter, establishes the squashed entanglement of a quantum channel as an upper bound on the quantum communication capacity of any channel assisted by unlimited forward and backward classical communication. A similar proof establishes this quantity as an upper bound on the private capacity of a quantum channel assisted by unlimited forward and backward public classical communication. This latter result is relevant as a limitation on rates achievable in quantum key distribution. As an important application, we determine that these capacities can never exceed log((1+η)/(1-η)) for a pure-loss bosonic channel for which a fraction η of the input photons make it to the output on average. The best known lower bound on these capacities is equal to log(1/(1-η)). Thus, in the high-loss regime for which η ≪ 1, this new upper bound demonstrates that the protocols corresponding to the above lower bound are nearly optimal.

Original languageEnglish (US)
Article number6832533
Pages (from-to)4987-4998
Number of pages12
JournalIEEE Transactions on Information Theory
Volume60
Issue number8
DOIs
StatePublished - Aug 2014
Externally publishedYes

Keywords

  • Squashed entanglement
  • private states
  • pure-loss bosonic channel
  • quantum capacity
  • quantum key distribution
  • secret key agreement capacity

ASJC Scopus subject areas

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences

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