Papers by Hermann Kampermann
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Danksagung Ich danke Herrn Prof. Dr. Wiebren S. Veeman für dieÜberlassung dieses interessanten Th... more Danksagung Ich danke Herrn Prof. Dr. Wiebren S. Veeman für dieÜberlassung dieses interessanten Themas und für die Gestaltungsfreiräume bei der Wahl der Forschungsausrichtung. Insbesondere danke ich für die Möglichkeiten, an verschiedenen Konferenzen und an der Fermi Sommerschule teilgenommen haben zu dürfen. Von Ihnen ist so das Fundament der Arbeit geschaffen worden. Herrn Prof. PhD. Volker Buß danke ich nicht nur für dieÜbernahme des Korreferats, sondern auch für die Unterstützung während des Studiums. Die theoretische Chemie war die ganze Zeitüber wie ein zweites Zuhause. Ich danke Manfred Zähres für die vielen Hilfestellungen im Bereich der NMR. Für die Lösung technischer Probleme danke ich Uwe Bachorski, Stefanie Dehne, Manfred Meier und Kirsten Schwark. Für die angenehme Atmosphäre in der Arbeitsgruppe danke ich Dr. Martin Horstmann, Annegret Terheiden, Christiane Finder, Natascha Schürks (jetzt Emmerichs), Dr. Holger Schmidt, Dr. Daniel Lattner, Wassef Al Sekhaneh, Dr. Mrignayani Kotecha und alle anderen Mitgliedern der physikalischen Chemie. Dem Korrekturmeister Christian Galle danke ich für die mühsame Arbeit mit dieser Dissertation und für das Ertragen einiger Nickeligkeiten als Bürokompagnon. Insbesondere möchte ich mich bei Karsten Koppe, Christoph Breitenstein und Marko Schreiber für die Freundschaft bedanken. Nach dem Motto die wichtigsten Worte kommen zum Schluss, danke ich meiner Frau Barbara und meinem Sohn Jonas für das immense Verständnis der vielen Arbeit.
Danksagung Ich danke Herrn Prof. Dr. Wiebren S. Veeman für dieÜberlassung dieses interessanten Th... more Danksagung Ich danke Herrn Prof. Dr. Wiebren S. Veeman für dieÜberlassung dieses interessanten Themas und für die Gestaltungsfreiräume bei der Wahl der Forschungsausrichtung. Insbesondere danke ich für die Möglichkeiten, an verschiedenen Konferenzen und an der Fermi Sommerschule teilgenommen haben zu dürfen. Von Ihnen ist so das Fundament der Arbeit geschaffen worden. Herrn Prof. PhD. Volker Buß danke ich nicht nur für dieÜbernahme des Korreferats, sondern auch für die Unterstützung während des Studiums. Die theoretische Chemie war die ganze Zeitüber wie ein zweites Zuhause. Ich danke Manfred Zähres für die vielen Hilfestellungen im Bereich der NMR. Für die Lösung technischer Probleme danke ich Uwe Bachorski, Stefanie Dehne, Manfred Meier und Kirsten Schwark. Für die angenehme Atmosphäre in der Arbeitsgruppe danke ich Dr. Martin Horstmann, Annegret Terheiden, Christiane Finder, Natascha Schürks (jetzt Emmerichs), Dr. Holger Schmidt, Dr. Daniel Lattner, Wassef Al Sekhaneh, Dr. Mrignayani Kotecha und alle anderen Mitgliedern der physikalischen Chemie. Dem Korrekturmeister Christian Galle danke ich für die mühsame Arbeit mit dieser Dissertation und für das Ertragen einiger Nickeligkeiten als Bürokompagnon. Insbesondere möchte ich mich bei Karsten Koppe, Christoph Breitenstein und Marko Schreiber für die Freundschaft bedanken. Nach dem Motto die wichtigsten Worte kommen zum Schluss, danke ich meiner Frau Barbara und meinem Sohn Jonas für das immense Verständnis der vielen Arbeit.
It is well known that the classification of pure multiparticle entangled states according to stoc... more 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.
Page 1. arXiv:0807.3923v2 [quant-ph] 9 Mar 2010 Unambiguous discrimination of mixed quantum state... more Page 1. arXiv:0807.3923v2 [quant-ph] 9 Mar 2010 Unambiguous discrimination of mixed quantum states: optimal solution and case study Matthias Kleinmann,1, 2, ∗ Hermann Kampermann,1 and Dagmar Bruß1 1Institut für ...
We study eavesdropping in quantum key distribution with the six state protocol, when the signal s... more We study eavesdropping in quantum key distribution with the six state protocol, when the signal states are mixed with white noise. This situation may arise either when Alice deliberately adds noise to the signal states before they leave her lab, or in a realistic scenario where Eve cannot replace the noisy quantum channel by a noiseless one. We find Eve's optimal mutual information with Alice, for individual attacks, as a function of the qubit error rate. Our result is that added quantum noise can make quantum key distribution more robust against eavesdropping.
Physical Review A
We introduce the concept of a physical process that purifies a mixed quantum state, taken from a ... more We introduce the concept of a physical process that purifies a mixed quantum state, taken from a set of states, and investigate the conditions under which such a purification map exists. Here, a purification of a mixed quantum state is a pure state in a higher-dimensional Hilbert space, the reduced density matrix of which is identical to the original state. We characterize all sets of mixed quantum states, for which perfect purification is possible. Surprisingly, some sets of two non-commuting states are among them. Furthermore, we investigate the possibility of performing an imperfect purification.
We revisit the problem of discriminating orthogonal quantum states within the local quantum opera... more We revisit the problem of discriminating orthogonal quantum states within the local quantum operation and classical communication (LOCC) paradigm. Our particular focus is on the asymptotic situation where the parties have infinite resources and the protocol may become arbitrarily long. Our main result is a necessary condition for perfect asymptotic LOCC discrimination. As an application, we prove that for complete
The six-state protocol is a discrete-variable protocol for quantum key distribution, that permits... more 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.© (2011) COPYRIGHT Society of Photo-Optical Instrumentation...
In quantum information theory, the reliable and effective detection of entanglement is of paramou... more In quantum information theory, the reliable and effective detection of entanglement is of paramount importance. However, given an unknown state, assessing its entanglement is a challenging task. To attack this problem, we investigate the use of random local measurements, from which entanglement witnesses are then constructed via semidefinite programming methods. We propose a scheme of successively increasing the number of measurements until the presence of entanglement can be unambiguously concluded, and investigate its performance in various examples.
We show how general graph states, an important resource state for multipartite quantum protocols,... more We show how general graph states, an important resource state for multipartite quantum protocols, can be distributed over large distances using intermediate repeater stations. To this aim we describe a one way quantum repeater scheme using encoding in the language of graph states. For a general Calderbank-Shor-Steane (CSS) code we do a refined error analysis that allows to correct qubit errors and erasures caused by imperfect preparation, gates, transmission, detection, etc.. We analyze the cost and repeater rate for this general scheme. The concept is exemplified by the 7-qubit Steane code and the quantum Golay code.
Entanglement is a ubiquitous feature of low temperature systems and believed to be highly relevan... more Entanglement is a ubiquitous feature of low temperature systems and believed to be highly relevant for the dynamics of condensed matter properties and quantum computation even at higher temperatures. The experimental certification of this paradigmatic quantum effect in macroscopic high temperature systems is constrained by the limited access to the quantum state of the system. In this paper we show how macroscopic observables beyond the energy of the system can be exploited as proxy witnesses for entanglement detection. Using linear and semi-definite relaxations we show that all previous approaches to this problem can be outperformed by our proxies, i.e. entanglement can be certified at higher temperatures without access to any local observable. For an efficient computation of proxy witnesses one can resort to a generalized grand canonical ensemble, enabling entanglement certification even in complex systems with macroscopic particle numbers.
Physical Review A
We develop a new method to quantify the secret key rate for permutation-invariant protocols for c... more 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.
Journal of Physics A Mathematical and Theoretical
We consider a subclass of bipartite CHSH-type Bell inequalities. We investigate operations, which... more We consider a subclass of bipartite CHSH-type Bell inequalities. We investigate operations, which leave their Tsirelson bound invariant, but change their classical bound. The optimal observables are unaffected except for a relative rotation of the two laboratories. We illustrate the utility of these operations by giving explicit examples: We prove that for a fixed quantum state and fixed measurement setup except for a relative rotation of the two laboratories, there is a Bell inequality that is maximally violated for this rotation, and we optimise some Bell inequalities with respect to the maximal violation. Finally we optimise the qutrit to qubit ratio of some dimension witnessing Bell inequalities.
Many typical Bell experiments can be described as follows. A source repeatedly distributes partic... more Many typical Bell experiments can be described as follows. A source repeatedly distributes particles among two spacelike separated observers. Each of them makes a measurement, using an observable randomly chosen out of several possible ones, leading to one of two possible outcomes. After collecting a sufficient amount of data one calculates the value of a so-called Bell expression. An important question in this context is whether the result is compatible with bounds based on the assumptions of locality, realism and freedom of choice. Here we are interested in bounds on the obtained value derived from quantum theory, so-called Tsirelson bounds. We describe a simple Tsirelson bound, which is based on a singular value decomposition. This mathematical result leads to some physical insights. In particular the optimal observables can be obtained. Furthermore statements about the dimension of the underlying Hilbert space are possible. Finally, Bell inequalities can be modified to match rot...
Physical Review A
Quantum repeaters represent one possible way to achieve long-distance quantum key distribution. C... more 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.
Physical Review A
We investigate secret key rates for the quantum repeater using encoding [L. Jiang et al., Phys. R... more We investigate secret key rates for the quantum repeater using encoding [L. Jiang et al., Phys. Rev. A 79, 032325 (2009)] and compare them to the standard repeater scheme by Briegel, D\"ur, Cirac, and Zoller. The former scheme has the advantage of a minimal consumption of classical communication. We analyze the trade-off in the secret key rate between the communication time and the required resources. For this purpose, we introduce an error model for the repeater using encoding which allows for input Bell states with a fidelity smaller than one, in contrast to the model given in [L. Jiang et al., Phys. Rev. A 79, 032325 (2009)]. We show that one can correct additional errors in the encoded connection procedure of this repeater and develop a suitable decoding algorithm. Furthermore, we derive the rate of producing entangled pairs for the quantum repeater using encoding and give the minimal parameters (gate quality and initial fidelity) for establishing a nonzero secret key. We f...
Physical Review A
We generalize measurement-device-independent quantum key distribution [ H.-K. Lo, M. Curty, and B... more 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.
Physical Review Letters
We present a simple analytic bound on the quantum value of general correlation type Bell inequali... more We present a simple analytic bound on the quantum value of general correlation type Bell inequalities, similar to Tsirelson's bound. It is based on the maximal singular value of the coefficient matrix associated with the inequality. We provide a criterion for tightness of the bound and show that the class of inequalities where our bound is tight covers many famous examples from the literature. We describe how this bound helps to construct Bell inequalities, in particular inequalities that witness the dimension of the measured observables.
Physical Review A
Entanglement distribution with separable states has recently attracted considerable attention. Re... more 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.
Physical Review B, 2014
We show how the entanglement contained in states of spins arranged on a lattice may be quantified... more We show how the entanglement contained in states of spins arranged on a lattice may be quantified with observables arising in scattering experiments. We focus on the partial differential cross-section obtained in neutron scattering from magnetic materials but our results are sufficiently general such that they may also be applied to, e.g., optical Bragg scattering from ultracold atoms in optical lattices or from ion chains. We discuss resonating valence bond states and ground and thermal states of experimentally relevant models-such as Heisenberg, Majumdar-Ghosh, and XY models-in different geometries and with different spin numbers. As a by-product, we find that for the one-dimensional XY model in a transverse field such measurements reveal factorization and the quantum phase transition at zero temperature.
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Papers by Hermann Kampermann