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arXiv · 1707.05543

Versatile relative entropy bounds for quantum networks

Luca Rigovacca·Go Kato·Stefan Bäuml·M. S. Kim·W. J. Munro·Koji Azuma
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Abstract

We provide a versatile upper bound on the number of maximally entangled qubits, or private bits, shared by two parties via a generic adaptive communication protocol over a quantum network when the use of classical communication is not restricted. Although our result follows the idea of Azuma et al. [Nat. Comm. 7, 13523 (2016)] of splitting the network into two parts, our approach relaxes their strong restriction, consisting of the use of a single entanglement measure in the quantification of the maximum amount of entanglement generated by the channels. In particular, in our bound the measure can be chosen on a channel-by-channel basis, in order to make it as tight as possible. This enables us to apply the relative entropy of entanglement, which often gives a state-of-the-art upper bound, on every Choi-simulable channel in the network, even when the other channels do not satisfy this property. We also develop tools to compute, or bound, the max-relative entropy of entanglement for channels that are invariant under phase rotations. In particular, we present an analytical formula for the max-relative entropy of entanglement of the qubit amplitude damping channel.

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Luca Rigovacca, Go Kato, Stefan Bäuml, M. S. Kim, W. J. Munro, Koji Azuma. 2018-01-27. Versatile relative entropy bounds for quantum networks. https://doi.org/10.1088/1367-2630%2Faa9fcf

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