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

• Published in: 2014 IEEE International Symposium on Information Theory pp. 326 - 330
• Main Authors: Takeoka, Masahiro, Guha, Saikat, Wilde, Mark M.
• Format: Conference Proceeding
• Language: English
• Published: IEEE 01.06.2014
• Subjects: Entropy; Mutual information; Protocols; Quantum entanglement; Upper bound
• ISSN: 2157-8095; 2157-8117
• DOI: 10.1109/ISIT.2014.6874848

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.