arXiv subjects

Hermann Kampermann

Publications and source records attributed to Hermann Kampermann.

At least 91 records · Page 5Linked to original sources

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

A review on super dense coding over covariant noisy channels

We study the performance of the super dense coding protocol in the presence of quantum channels with covariant noise. We first consider the bipartite case and review in a unified way the case of general Pauli channels. We discuss both the cases of unitary and non-unitary encoding. We also study the multipartite scenario and investigate the case of many senders and one receiver.

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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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arXiv2012

Distributed super dense coding over noisy channels

We study multipartite super dense coding in the presence of a covariant noisy channel. We investigate the case of many senders and one receiver, considering both unitary and non-unitary encoding. We study the scenarios where the senders apply local encoding or global encoding. We show that, up to some pre-processing on the original state, the senders cannot do better encoding than local, unitary encoding. We then introduce general Pauli channels as a significant example of covariant maps. Considering Pauli channels, we provide examples for which the super dense coding capacity is explicitly determined.

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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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arXiv2010

Linking a distance measure of entanglement to its convex roof

An important problem in quantum information theory is the quantification of entanglement in multipartite mixed quantum states. In this work, a connection between the geometric measure of entanglement and a distance measure of entanglement is established. We present a new expression for the geometric measure of entanglement in terms of the maximal fidelity with a separable state. A direct application of this result provides a closed expression for the Bures measure of entanglement of two qubits. We also prove that the number of elements in an optimal decomposition w.r.t. the geometric measure of entanglement is bounded from above by the Caratheodory bound, and we find necessary conditions for the structure of an optimal decomposition.

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