arXiv subjects

Otfried Gühne

Publications and source records attributed to Otfried Gühne.

At least 181 records · Page 10Linked to original sources

arXiv2013

Device-independent entanglement quantification and related applications

We present a general method to quantify both bipartite and multipartite entanglement in a device-independent manner, meaning that we put a lower bound on the amount of entanglement present in a system based on observed data only but independently of any quantum description of the employed devices. Some of the bounds we obtain, such as for the Clauser-Horne-Shimony-Holt Bell inequality or the Svetlichny inequality, are shown to be tight. Besides, device-independent entanglement quantification can serve as a basis for numerous tasks. We show in particular that our method provides a rigorous way to construct dimension witnesses, gives new insights into the question whether bound entangled states can violate a Bell inequality, and can be used to construct device independent entanglement witnesses involving an arbitrary number of parties.

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arXiv2013

Certifying experimental errors in quantum experiments

When experimental errors are ignored in an experiment, the subsequent analysis of its results becomes questionable. We develop tests to detect systematic errors in quantum experiments where only a finite amount of data is recorded and apply these tests to tomographic data taken in an ion trap experiment. We put particular emphasis on quantum state tomography and present three detection methods: the first two employ linear inequalities while the third is based on the generalized likelihood ratio.

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arXiv2013

Genuine multiparticle entanglement of permutationally invariant states

We consider the problem of characterizing genuine multiparticle entanglement for permutationally invariant states using the approach of PPT mixtures. We show that the evaluation of this necessary biseparability criterion scales polynomially with the number of particles. In practice, it can be evaluated easily up to ten qubits and improves existing criteria significantly. Finally, we show that our approach solves the problem of characterizing genuine multiparticle entanglement for permutationally invariant three-qubit states.

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arXiv2012

Computing complexity measures for quantum states based on exponential families

Given a multiparticle quantum state, one may ask whether it can be represented as a thermal state of some Hamiltonian with k-particle interactions only. The distance from the exponential family defined by these thermal states can be considered as a measure of complexity of a given state. We investigate the resulting optimization problem and show how symmetries can be exploited to simplify the task of finding the nearest thermal state in a given exponential family. We also present an algorithm for the computation of the complexity measure and consider specific examples to demonstrate its applicability.

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arXiv2012

Estimating entanglement monotones with a generalization of the Wootters formula

Entanglement monotones, such as the concurrence, are useful tools to characterize quantum correlations in various physical systems. The computation of the concurrence involves, however, difficult optimizations and only for the simplest case of two qubits a closed formula was found by Wootters [Phys. Rev. Lett. 80, 2245 (1998)]. We show how this approach can be generalized, resulting in lower bounds on the concurrence for higher dimensional systems as well as for multipartite systems. We demonstrate that for certain families of states our results constitute the strongest bipartite entanglement criterion so far; moreover, they allow to recognize novel families of multiparticle bound entangled states.

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arXiv2012

Optimal inequalities for state-independent contextuality

Contextuality is a natural generalization of nonlocality which does not need composite systems or spacelike separation and offers a wider spectrum of interesting phenomena. Most notably, in quantum mechanics there exist scenarios where the contextual behavior is independent of the quantum state. We show that the quest for an optimal inequality separating quantum from classical noncontextual correlations in an state-independent manner admits an exact solution, as it can be formulated as a linear program. We introduce the noncontextuality polytope as a generalization of the locality polytope, and apply our method to identify two different tight optimal inequalities for the most fundamental quantum scenario with state-independent contextuality.

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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

Permutationally invariant state reconstruction

Feasible tomography schemes for large particle numbers must possess, besides an appropriate data acquisition protocol, also an efficient way to reconstruct the density operator from the observed finite data set. Since state reconstruction typically requires the solution of a non-linear large-scale optimization problem, this is a major challenge in the design of scalable tomography schemes. Here we present an efficient state reconstruction scheme for permutationally invariant quantum state tomography. It works for all common state-of-the-art reconstruction principles, including, in particular, maximum likelihood and least squares methods, which are the preferred choices in today's experiments. This high efficiency is achieved by greatly reducing the dimensionality of the problem employing a particular representation of permutationally invariant states known from spin coupling combined with convex optimization, which has clear advantages regarding speed, control and accuracy in comparison to commonly employed numerical routines. First prototype implementations easily allow reconstruction of a state of 20 qubits in a few minutes on a standard computer.

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arXiv2012

Complexity measures, emergence, and multiparticle correlations

We study correlation measures for complex systems. First, we investigate some recently proposed measures based on information geometry. We show that these measures can increase under local transformations as well as under discarding particles, thereby questioning their interpretation as a quantifier for complexity or correlations. We then propose a refined definition of these measures, investigate its properties and discuss its numerical evaluation. As an example, we study coupled logistic maps and study the behavior of the different measures for that case. Finally, we investigate other local effects during the coarse graining of the complex system.

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arXiv2012

Entropic uncertainty relations and the stabilizer formalism

Entropic uncertainty relations express the quantum mechanical uncertainty principle by quantifying uncertainty in terms of entropy. Central questions include the derivation of lower bounds on the total uncertainty for given observables, the characterization of observables that allow strong uncertainty relations, and the construction of such relations for the case of several observables. We demonstrate how the stabilizer formalism can be applied to these questions. We show that the Maassen-Uffink entropic uncertainty relation is tight for the measurement in any pair of stabilizer bases. We compare the relative strengths of variance-based and various entropic uncertainty relations for dichotomic anticommuting observables.

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arXiv2011

Multiparticle entanglement in graph-diagonal states: Necessary and sufficient conditions for four qubits

The characterization of genuine multiparticle entanglement is important for entanglement theory as well as experimental studies related to quantum information theory. Here, we completely characterize genuine multiparticle entanglement for four-qubit states diagonal in the cluster-state basis. In addition, we give a complete characterization of multiparticle entanglement for all five-qubit graph states mixed with white noise, for states diagonal in the basis corresponding to the five-qubit Y-shaped graph, and for a family of graph states with an arbitrary number of qubits.

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arXiv2011

Memory cost of quantum contextuality

The simulation of quantum effects requires certain classical resources, and quantifying them is an important step in order to characterize the difference between quantum and classical physics. For a simulation of the phenomenon of state-independent quantum contextuality, we show that the minimal amount of memory used by the simulation is the critical resource. We derive optimal simulation strategies for important cases and prove that reproducing the results of sequential measurements on a two-qubit system requires more memory than the information carrying capacity of the system.

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arXiv2011

Entanglement Witnesses for Graph States: General Theory and Examples

We present a general theory for the construction of witnesses that detect genuine multipartite entanglement in graph states. First, we present explicit witnesses for all graph states of up to six qubits which are better than all criteria so far. Therefore, lower fidelities are required in experiments that aim at the preparation of graph states. Building on these results, we develop analytical methods to construct two different types of entanglement witnesses for general graph states. For many classes of states, these operators exhibit white noise tolerances that converge to one when increasing the number of particles. We illustrate our approach for states such as the linear and the 2D cluster state. Finally, we study an entanglement monotone motivated by our approach for graph states.

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arXiv2011

Taming multiparticle entanglement

We present an approach to characterize genuine multiparticle entanglement using appropriate approximations in the space of quantum states. This leads to a criterion for entanglement which can easily be calculated using semidefinite programming and improves all existing approaches significantly. Experimentally, it can also be evaluated when only some observables are measured. Furthermore, it results in a computable entanglement monotone for genuine multiparticle entanglement. Based on this, we develop an analytical approach for the entanglement detection in cluster states, leading to an exponential improvement compared with existing schemes.

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arXiv2011

Experimental Test of Bell inequalities with Six-Qubit Graph States

We report on the experimental realization of two different Bell inequality tests based on six-qubit linear-type and Y-shape graph states. For each of these states, the Bell inequalities tested are optimal in the sense that they provide the maximum violation among all Bell inequalities with stabilizing observables and possess the maximum resistance to noise.

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arXiv2011

Entanglement criteria and full separability of multi-qubit quantum states

We introduce an entanglement criterion to exclude full separability of quantum states. We present numerical evidence that the criterion is necessary and sufficient for the class of GHZ diagonal three-qubit states and estimate the volume of bound entangled states within this class. Finally, we extend our approach to bound entangled states which are not GHZ diagonal.

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arXiv2010

Discrimination strategies for inequivalent classes of multipartite entangled states

How can one discriminate different inequivalent classes of multiparticle entanglement experimentally? We present an approach for the discrimination of an experimentally prepared state from the equivalence class of another state. We consider two possible measures for the discrimination strength of an observable. The first measure is based on the difference of expectation values, the second on the relative entropy of the probability distributions of the measurement outcomes. The interpretation of these measures and their usefulness for experiments with limited resources are discussed. In the case of graph states, the stabilizer formalism is employed to compute these quantities and to find sets of observables that result in the most decisive discrimination.

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arXiv2010

Not all pure entangled states are useful for sub shot-noise interferometry

We investigate the connection between the shot-noise limit in linear interferometers and particle entanglement. In particular, we ask whether or not sub shot-noise sensitivity can be reached with all pure entangled input states of $N$ particles if they can be optimized with local operations. Results on the optimal local transformations allow us to show that for $N=2$ all pure entangled states can be made useful for sub shot-noise interferometry while for $N>2$ this is not the case. We completely classify the useful entangled states available in a bosonic two-mode interferometer. We apply our results to several states, in particular to multi-particle singlet states and to cluster states. The latter turn out to be practically useless for sub shot-noise interferometry. Our results are based on the Cramer-Rao bound and the Fisher information.

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