34,884 research outputs found

    Secret Message Transmission over Quantum Channels under Adversarial Quantum Noise: Secrecy Capacity and Super-Activation

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    We determine the secrecy capacities of AVQCs (arbitrarily varying quantum channels). Both secrecy capacity with average error probability and with maximal error probability are derived. Both derivations are based on one common code construction. The code we construct fulfills a stringent secrecy requirement, which is called the strong code concept. We determine when the secrecy capacity is a continuous function of the system parameters and completely characterize its discontinuity points both for average error criterion and for maximal error criterion. Furthermore, we prove the phenomenon "super-activation" for secrecy capacities of AVQCs, i.e., two quantum channels both with zero secrecy capacity, which, if used together, allow secure transmission with positive capacity. We also discuss the relations between the entanglement distillation capacity, the entanglement generating capacity, and the strong subspace transmission capacity for AVQCs.Comment: arXiv admin note: text overlap with arXiv:1702.0348

    Quantum capacity under adversarial quantum noise: arbitrarily varying quantum channels

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    We investigate entanglement transmission over an unknown channel in the presence of a third party (called the adversary), which is enabled to choose the channel from a given set of memoryless but non-stationary channels without informing the legitimate sender and receiver about the particular choice that he made. This channel model is called arbitrarily varying quantum channel (AVQC). We derive a quantum version of Ahlswede's dichotomy for classical arbitrarily varying channels. This includes a regularized formula for the common randomness-assisted capacity for entanglement transmission of an AVQC. Quite surprisingly and in contrast to the classical analog of the problem involving the maximal and average error probability, we find that the capacity for entanglement transmission of an AVQC always equals its strong subspace transmission capacity. These results are accompanied by different notions of symmetrizability (zero-capacity conditions) as well as by conditions for an AVQC to have a capacity described by a single-letter formula. In he final part of the paper the capacity of the erasure-AVQC is computed and some light shed on the connection between AVQCs and zero-error capacities. Additionally, we show by entirely elementary and operational arguments motivated by the theory of AVQCs that the quantum, classical, and entanglement-assisted zero-error capacities of quantum channels are generically zero and are discontinuous at every positivity point.Comment: 49 pages, no figures, final version of our papers arXiv:1010.0418v2 and arXiv:1010.0418. Published "Online First" in Communications in Mathematical Physics, 201
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