21,273 research outputs found

    The quantum capacity with symmetric side channels

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    We present an upper bound for the quantum channel capacity that is both additive and convex. Our bound can be interpreted as the capacity of a channel for high-fidelity quantum communication when assisted by a family of channels that have no capacity on their own. This family of assistance channels, which we call symmetric side channels, consists of all channels mapping symmetrically to their output and environment. The bound seems to be quite tight, and for degradable quantum channels it coincides with the unassisted channel capacity. Using this symmetric side channel capacity, we find new upper bounds on the capacity of the depolarizing channel. We also briefly indicate an analogous notion for distilling entanglement using the same class of (one-way) channels, yielding one of the few entanglement measures that is monotonic under local operations with one-way classical communication (1-LOCC), but not under the more general class of local operations with classical communication (LOCC).Comment: 10 pages, 4 figure

    Public Quantum Communication and Superactivation

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    Is there a meaningful quantum counterpart to public communication? We argue that the symmetric-side channel -- which distributes quantum information symmetrically between the receiver and the environment -- is a good candidate for a notion of public quantum communication in entanglement distillation and quantum error correction. This connection is partially motivated by [Brand\~ao and Oppenheim, arXiv:1004.3328], where it was found that if a sender would like to communicate a secret message to a receiver through an insecure quantum channel using a shared quantum state as a key, then the insecure quantum channel is only ever used to simulate a symmetric-side channel, and can always be replaced by it without altering the optimal rate. Here we further show, in complete analogy to the role of public classical communication, that assistance by a symmetric-side channel makes equal the distillable entanglement, the recently-introduced mutual independence, and a generalization of the latter, which quantifies the extent to which one of the parties can perform quantum privacy amplification. Symmetric-side channels, and the closely related erasure channel, have been recently harnessed to provide examples of superactivation of the quantum channel capacity. Our findings give new insight into this non-additivity of the channel capacity and its relation to quantum privacy. In particular, we show that single-copy superactivation protocols with the erasure channel, which encompasses all examples of non-additivity of the quantum capacity found to date, can be understood as a conversion of mutual independence into distillable entanglement.Comment: 10 page

    Game-theoretic characterization of antidegradable channels

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    We introduce a guessing game involving a quantum channel, three parties - the sender, the receiver and an eavesdropper, Eve - and a quantum public side channel. We prove that a necessary and sufficient condition for the quantum channel to be antidegradable, is that Eve wins the game. We thus obtain a complete operational characterization of antidegradable channels in a game-theoretic framework.Comment: v2: published version, 14 pages, 1 figure; v1: 13 pages, 1 figur

    Private Quantum Coding for Quantum Relay Networks

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    The relay encoder is an unreliable probabilistic device which is aimed at helping the communication between the sender and the receiver. In this work we show that in the quantum setting the probabilistic behavior can be completely eliminated. We also show how to combine quantum polar encoding with superactivation-assistance in order to achieve reliable and capacity-achieving private communication over noisy quantum relay channels.Comment: 15 pages, 3 figures, Journal-ref: Lecture Notes in Computer Science, Vol. 7479, pp. 239-250. Springer-Verlag, 2012, presented in part at the 11th Intl. Conference on Quantum Communication, Measurement and Computing (QCMC2012), v2: minor formatting change
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