arXiv subjects

Dagmar Bruß

Publications and source records attributed to Dagmar Bruß.

At least 91 records · Page 5Linked to original sources

arXiv2013

Finite-range multiplexing enhances quantum key distribution via quantum repeaters

Quantum repeaters represent one possible way to achieve long-distance quantum key distribution. Collins et al. in [Phys. Rev. Lett. 98, 060502 (2007)] proposed multiplexing as method to increase the repeater rate and to decrease the requirement in memory coherence time. Motivated by the experimental fact that long-range connections are practically demanding, in this paper we extend the original quantum repeater multiplexing protocol to the case of short-range connection. We derive analytical formulas for the repeater rate and we show that for short connection lengths it is possible to have most of the benefits of a full-range multiplexing protocol. Then we incorporate decoherence of quantum memories and we study the optimal matching for the Bell-state measurement protocol permitting to minimize memory requirements. Finally, we calculate the secret key rate and we show that the improvement via finite-range multiplexing is of the same order of magnitude as via full-range multiplexing.

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arXiv2013

Limits for entanglement distribution with separable states

Entanglement distribution with separable states has recently attracted considerable attention. Recent results suggest that quantum discord - a measure for quantum correlations beyond entanglement - is responsible for this counterintuitive phenomenon. In this work we study this question from a different perspective, and find minimal requirements for a separable state to be useful for entanglement distribution. Surprisingly, we find that the presence of quantum discord is not sufficient to ensure entanglement distribution: there exist states with nonzero quantum discord which nevertheless cannot be used for entanglement distribution. As a result, we show that entanglement distribution is not possible with rank two separable states. Our work sheds new light on the task of entanglement distribution with separable states, and reveals a new classification of quantum states with respect to their usefulness for this task.

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arXiv2013

Quantum repeaters and quantum key distribution: analysis of secret key rates

We analyze various prominent quantum repeater protocols in the context of long-distance quantum key distribution. These protocols are the original quantum repeater proposal by Briegel, Dür, Cirac and Zoller, the so-called hybrid quantum repeater using optical coherent states dispersively interacting with atomic spin qubits, and the Duan-Lukin-Cirac-Zoller-type repeater using atomic ensembles together with linear optics and, in its most recent extension, heralded qubit amplifiers. For our analysis, we investigate the most important experimental parameters of every repeater component and find their minimally required values for obtaining a nonzero secret key. Additionally, we examine in detail the impact of device imperfections on the final secret key rate and on the optimal number of rounds of distillation when the entangled states are purified right after their initial distribution.

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arXiv2013

Measurement-device-independent quantum key distribution with quantum memories

We generalize measurement-device-independent quantum key distribution [ H.-K. Lo, M. Curty, and B. Qi, Phys. Rev. Lett. 108, 130503 (2012) ] to the scenario where the Bell-state measurement station contains also heralded quantum memories. We find analytical formulas, in terms of device imperfections, for all quantities entering in the secret key rates, i.e., the quantum bit error rate and the repeater rate. We assume either single-photon sources or weak coherent pulse sources plus decoy states. We show that it is possible to significantly outperform the original proposal, even in presence of decoherence of the quantum memory. Our protocol may represent the first natural step for implementing a two-segment quantum repeater.

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arXiv2013

Quantum repeaters and quantum key distribution: the impact of entanglement distillation on the secret key rate

We investigate quantum repeaters in the context of quantum key distribution. We optimize the secret key rate per memory per second with respect to different distillation protocols and distillation strategies. For this purpose, we also derive an analytical expression for the average number of entangled pairs created by the quantum repeater, including classical communication times for entanglement swapping and entanglement distillation. We investigate the impact of this classical communication time on the secret key rate. We finally study the effect of the detector efficiency on the secret key rate.

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arXiv2012

Algorithm for characterizing stochastic local operations and classical communication classes of multiparticle entanglement

It is well known that the classification of pure multiparticle entangled states according to stochastic local operations leads to a natural classification of mixed states in terms of convex sets. We present a simple algorithmic procedure to prove that a quantum state lies within a given convex set. Our algorithm generalizes a recent algorithm for proving separability of quantum states [J. Barreiro et al., Nature Phys. 6, 943 (2010)]. We give several examples which show the wide applicability of our approach. We also propose a procedure to determine a vicinity of a given quantum state which still belongs to the considered convex set.

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arXiv2012

Determining lower bounds on a measure of multipartite entanglement from few local observables

We introduce a method to lower bound an entropy-based measure of genuine multipartite entanglement via nonlinear entanglement witnesses. We show that some of these bounds are tight and explicitly work out their connection to a framework of nonlinear witnesses that were published recently. Furthermore we provide a detailed analysis of these lower bounds in the context of other possible bounds and measures. In exemplary cases we show that only a few local measurements are necessary to determine these lower bounds.

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arXiv2012

Secret key rates for coherent attacks

We develop a new method to quantify the secret key rate for permutation-invariant protocols for coherent attacks and finite resources. The method reduces the calculation of secret key rates for coherent attacks to the calculation for collective attacks by bounding the smooth min-entropy of permutation-invariant states via the smooth min-entropy of corresponding tensor-product states. The comparison of the results to the well-known post-selection technique for the BB84 and six-state protocol shows the high relevance of this method. Since our calculation of secret key rates for coherent attacks strongly depends on the way of treating collective attacks, a prospective progress in the analysis of collective attacks will immediately cause progress in our strategy.

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arXiv2012

Quantum cost for sending entanglement

Establishing quantum entanglement between two distant parties is an essential step of many protocols in quantum information processing. One possibility for providing long-distance entanglement is to create an entangled composite state within a lab and then physically send one subsystem to a distant lab. However, is this the "cheapest" way? Here, we investigate the minimal "cost" that is necessary for establishing a certain amount of entanglement between two distant parties. We prove that this cost is intrinsically quantum, and is specified by quantum correlations. Our results provide an optimal protocol for entanglement distribution and show that quantum correlations are the essential resource for this task.

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arXiv2011

Quantum key distribution with finite resources: Taking advantage of quantum noise

We compare the effect of different noise scenarios on the achievable rate of an epsilon-secure key for the BB84 and the six-state protocol. We study the situation where quantum noise is added deliberately, and investigate the remarkable benefit for the finite key rate. We compare our results to the known case of added classical noise and the asymptotic key rate, i.e. in the limit of infinitely many signals. As a complementary interpretation we show that under the realistic assumption that the noise which is unavoidably introduced by a real channel is not fully dedicated to the eavesdropper, the secret key rate increases significantly.

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arXiv2011

Finite-key analysis of the six-state protocol with photon-number-resolution detectors

The six-state protocol is a discrete-variable protocol for quantum key distribution, that permits to tolerate a noisier channel than the BB84 protocol. In this work we provide a lower bound on the maximum achievable key rate of a practical implementation of the entanglement-based version of the six-state protocol. Regarding the experimental set-up we consider that the source is untrusted and the photon-number statistics is measured using photon-number-resolving detectors. We provide the formula for the key rate for a finite initial number of resources. As an illustration of the considered formalism, we calculate the key rate for the setting where the source produces entangled photon pairs via parametric down-conversion and the losses in the channel depend on the distance. As a result we find that the finite-key corrections for the considered scenario are not negligible and they should be considered in any practical analysis.

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arXiv2011

Optimal super dense coding over memory channels

We study the super dense coding capacity in the presence of quantum channels with correlated noise. We investigate both the cases of unitary and non-unitary encoding. Pauli channels for arbitrary dimensions are treated explicitly. The super dense coding capacity for some special channels and resource states is derived for unitary encoding. We also provide an example of a memory channel where non-unitary encoding leads to an improvement in the super dense coding capacity.

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arXiv2011

Behavior of Quantum Correlations under Local Noise

We characterize the behavior of quantum correlations under the influence of local noisy channels. Intuition suggests that such noise should be detrimental for quantumness. When considering qubit systems, we show for which channel this is indeed the case: the amount of quantum correlations can only decrease under the action of unital channels. However, non-unital channels (e.g. such as dissipation) can create quantum correlations for some initially classical state. Furthermore, for higher-dimensional systems even unital channels may increase the amount of quantum correlations. Thus, counterintuitively, local decoherence can generate quantum correlations.

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arXiv2011

QKD with finite resources: secret key rates via Rényi entropies

A realistic Quantum Key Distribution (QKD) protocol necessarily deals with finite resources, such as the number of signals exchanged by the two parties. We derive a bound on the secret key rate which is expressed as an optimization problem over Rényi entropies. Under the assumption of collective attacks by an eavesdropper, a computable estimate of our bound for the six-state protocol is provided. This bound leads to improved key rates in comparison to previous results.

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arXiv2011

Linking Quantum Discord to Entanglement in a Measurement

We show that a von Neumann measurement on a part of a composite quantum system unavoidably creates distillable entanglement between the measurement apparatus and the system if the state has nonzero quantum discord. The minimal distillable entanglement is equal to the one-way information deficit. The quantum discord is shown to be equal to the minimal partial distillable entanglement that is the part of entanglement which is lost, when we ignore the subsystem which is not measured. We then show that any entanglement measure corresponds to some measure of quantum correlations. This powerful correspondence also yields necessary properties for quantum correlations. We generalize the results to multipartite measurements on a part of the system and on the total system.

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arXiv2011

Easy implementable algorithm for the geometric measure of entanglement

We present an easy implementable algorithm for approximating the geometric measure of entanglement from above. The algorithm can be applied to any multipartite mixed state. It involves only the solution of an eigenproblem and finding a singular value decomposition, no further numerical techniques are needed. To provide examples, the algorithm was applied to the isotropic states of 3 qubits and the 3-qubit XX model with external magnetic field.

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arXiv2011

Min-entropy and quantum key distribution: non-zero key rates for "small" numbers of signals

We calculate an achievable secret key rate for quantum key distribution with a finite number of signals, by evaluating the min-entropy explicitly. The min-entropy can be expressed in terms of the guessing probability, which we calculate for d-dimensional systems. We compare these key rates to previous approaches using the von Neumann entropy and find non-zero key rates for a smaller number of signals. Furthermore, we improve the secret key rates by modifying the parameter estimation step. Both improvements taken together lead to non-zero key rates for only 10^4-10^5 signals. An interesting conclusion can also be drawn from the additivity of the min-entropy and its relation to the guessing probability: for a set of symmetric tensor product states the optimal minimum-error discrimination (MED) measurement is the optimal MED measurement on each subsystem.

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arXiv2011

Experimentally implementable criteria revealing substructures of genuine multipartite entanglement

We present a general framework that reveals substructures of genuine multipartite entanglement. Via simple inequalities it is possible to discriminate different sets of multipartite qubit states. These inequalities are beneficial regarding experimental examinations as only local measurements are required. Furthermore, the number of observables scales favorably with system size. In exemplary cases we demonstrate the noise resistance and discuss implementations.

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