The squashed entanglement of a quantum channel
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, 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+eta)/(1eta)) for a pureloss bosonic channel for which a fraction eta of the input photons make it to the output on average. The best known lower bound on these capacities is equal to log(1/(1eta)). Thus, in the highloss regime for which eta << 1, this new upper bound demonstrates that the protocols corresponding to the above lower bound are nearly optimal.
 Publication:

arXiv eprints
 Pub Date:
 September 2013
 arXiv:
 arXiv:1310.0129
 Bibcode:
 2013arXiv1310.0129T
 Keywords:

 Quantum Physics;
 Computer Science  Information Theory
 EPrint:
 v3: 25 pages, 3 figures, significant expansion of paper