The squashed entanglement of a quantum channel

Masahiro Takeoka, Saikat Guha, Mark M. Wilde

Research output: Contribution to journalArticle

50 Citations (Scopus)

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

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Quantum communication
Quantum cryptography
Communication
Tensors
communication
Photons
recipient
regime

Keywords

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

ASJC Scopus subject areas

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

Cite this

The squashed entanglement of a quantum channel. / Takeoka, Masahiro; Guha, Saikat; Wilde, Mark M.

In: IEEE Transactions on Information Theory, Vol. 60, No. 8, 6832533, 08.2014, p. 4987-4998.

Research output: Contribution to journalArticle

Takeoka, Masahiro ; Guha, Saikat ; Wilde, Mark M. / The squashed entanglement of a quantum channel. In: IEEE Transactions on Information Theory. 2014 ; Vol. 60, No. 8. pp. 4987-4998.
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