7,592 research outputs found

    Average output entropy for quantum channels

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    We study the regularized average Renyi output entropy \bar{S}_{r}^{\reg} of quantum channels. This quantity gives information about the average noisiness of the channel output arising from a typical, highly entangled input state in the limit of infinite dimensions. We find a closed expression for \beta_{r}^{\reg}, a quantity which we conjecture to be equal to \Srreg. We find an explicit form for \beta_{r}^{\reg} for some entanglement-breaking channels, and also for the qubit depolarizing channel Δλ\Delta_{\lambda} as a function of the parameter λ\lambda. We prove equality of the two quantities in some cases, in particular we conclude that for Δλ\Delta_{\lambda} both are non-analytic functions of the variable λ\lambda.Comment: 32 pages, several plots and figures; positivity condition added for Theorem on entanglement breaking channels; new result for entrywise positive channel

    Standard super-activation for Gaussian channels requires squeezing

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    The quantum capacity of bosonic Gaussian quantum channels can be non-additive in a particularly striking way: a pair of such optical-fiber type channels can individually have zero quantum capacity but super-activate each other such that the combined channel has strictly positive capacity. This has been shown in [Nature Photonics 5, 624 (2011)] where it was conjectured that squeezing is a necessary resource for this phenomenon. We provide a proof of this conjecture by showing that for gauge covariant channels a Choi matrix with positive partial transpose implies that the channel is entanglement-breaking. In addition, we construct an example which shows that this implication fails to hold for Gaussian channels which arise from passive interactions with a squeezed environment.Comment: 5 pages, close to published versio

    Trade-off coding for universal qudit cloners motivated by the Unruh effect

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    A "triple trade-off" capacity region of a noisy quantum channel provides a more complete description of its capabilities than does a single capacity formula. However, few full descriptions of a channel's ability have been given due to the difficult nature of the calculation of such regions---it may demand an optimization of information-theoretic quantities over an infinite number of channel uses. This work analyzes the d-dimensional Unruh channel, a noisy quantum channel which emerges in relativistic quantum information theory. We show that this channel belongs to the class of quantum channels whose capacity region requires an optimization over a single channel use, and as such is tractable. We determine two triple-trade off regions, the quantum dynamic capacity region and the private dynamic capacity region, of the d-dimensional Unruh channel. Our results show that the set of achievable rate triples using this coding strategy is larger than the set achieved using a time-sharing strategy. Furthermore, we prove that the Unruh channel has a distinct structure made up of universal qudit cloning channels, thus providing a clear relationship between this relativistic channel and the process of stimulated emission present in quantum optical amplifiers.Comment: 26 pages, 4 figures; v2 has minor corrections to Definition 2. Definition 4 and Remark 5 have been adde

    Information capacity of quantum observable

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    In this paper we consider the classical capacities of quantum-classical channels corresponding to measurement of observables. Special attention is paid to the case of continuous observables. We give the formulas for unassisted and entanglement-assisted classical capacities C,CeaC,C_{ea} and consider some explicitly solvable cases which give simple examples of entanglement-breaking channels with C<Cea.C<C_{ea}. We also elaborate on the ensemble-observable duality to show that CeaC_{ea} for the measurement channel is related to the χ\chi-quantity for the dual ensemble in the same way as CC is related to the accessible information. This provides both accessible information and the χ\chi-quantity for the quantum ensembles dual to our examples.Comment: 13 pages. New section and references are added concerning the ensemble-observable dualit

    Probing the quantumness of channels with mixed states

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    We present an alternative approach to the derivation of benchmarks for quantum channels, such as memory or teleportation channels. Using the concept of effective entanglement and the verification thereof, a testing procedure is derived which demands very few experimental resources. The procedure is generalized by allowing for mixed test states. By constructing optimized measure & re-prepare channels, the benchmarks are found to be very tight in the considered experimental regimes.Comment: 11 Pages, 9 Figures, published versio
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