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Relative Entropy Bounds on Quantum, Private and Repeater Capacities

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Abstract

We find a strong-converse bound on the private capacity of a quantum channel assisted by unlimited two-way classical communication. The bound is based on the max-relative entropy of entanglement and its proof uses a new inequality for the sandwiched Rényi divergences based on complex interpolation techniques. We provide explicit examples of quantum channels where our bound improves upon both the transposition bound (on the quantum capacity assisted by classical communication) and the bound based on the squashed entanglement. As an application, we study a repeater version of the private capacity assisted by classical communication and provide an example of a quantum channel with high private capacity but negligible private repeater capacity.

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Authors and Affiliations

  1. QMATH, Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, 2100, Copenhagen, Denmark

    Matthias Christandl & Alexander Müller-Hermes

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  1. Matthias Christandl
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  2. Alexander Müller-Hermes
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Correspondence to Alexander Müller-Hermes.

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Communicated by M. M. Wolf

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Christandl, M., Müller-Hermes, A. Relative Entropy Bounds on Quantum, Private and Repeater Capacities. Commun. Math. Phys. 353, 821–852 (2017). https://doi.org/10.1007/s00220-017-2885-y

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  • DOI: https://doi.org/10.1007/s00220-017-2885-y

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