Title

Squashed entanglement and the two-way assisted capacities of a quantum channel

Document Type

Conference Proceeding

Publication Date

1-1-2014

Abstract

We define 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, Winter, et al., 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. © 2014 IEEE.

Publication Source (Journal or Book title)

IEEE International Symposium on Information Theory - Proceedings

First Page

326

Last Page

330

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