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. © 2014 IEEE.
Publication Source (Journal or Book title)
IEEE Transactions on Information Theory
Takeoka, M., Guha, S., & Wilde, M. (2014). The squashed entanglement of a quantum channel. IEEE Transactions on Information Theory, 60 (8), 4987-4998. https://doi.org/10.1109/TIT.2014.2330313