arXiv subjects

Otfried Gühne

Publications and source records attributed to Otfried Gühne.

At least 199 records · Page 11Linked to original sources

arXiv2010

Multiparticle covariance matrices and the impossibility of detecting graph state entanglement with two-particle correlations

We present a criterion for multiparticle entanglement based on covariance matrices. On the one hand, the criterion allows to detect bound entangled states which are not detected by other criteria; on the other hand, some strongly entangled pure states such as the GHZ states are not detected. We show, however, that this is a general phenomenon: No separability criterion based on two-particle correlations can recognize the entanglement in the family of graph states, to which the GHZ states belong.

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arXiv2010

Separability criteria for genuine multiparticle entanglement

We present a method to derive separability criteria for the different classes of multiparticle entanglement, especially genuine multiparticle entanglement. The resulting criteria are necessary and sufficient for certain families of states. Further, the criteria are superior to all known entanglement criteria for many other families; also they allow the detection of bound entanglement. We next demonstrate that they are easily implementable in experiments and discuss applications to the decoherence of multiparticle entangled states.

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arXiv2010

Experimental Realization of a Controlled-NOT Gate with Four-Photon Six-Qubit Cluster States

We experimentally demonstrate an optical controlled-NOT (CNOT) gate with arbitrary single inputs based on a 4-photon 6-qubit cluster state entangled both in polarization and spatial modes. We first generate the 6-qubit state, and then by performing single-qubit measurements the CNOT gate is applied to arbitrary single input qubits. To characterize the performance of the gate, we estimate its quantum process fidelity and prove its entangling capability. The results show that the gate cannot be reproduced by local operations and classical communication. Our experiment shows that cluster states are promising candidates for efficient optical quantum computation.

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arXiv2010

Increasing the statistical significance of entanglement detection in experiments

Entanglement is often verified by a violation of an inequality like a Bell inequality or an entanglement witness. Considerable effort has been devoted to the optimization of such inequalities in order to obtain a high violation. We demonstrate theoretically and experimentally that such an optimization does not necessarily lead to a better entanglement test, if the statistical error is taken into account. Theoretically, we show for different error models that reducing the violation of an inequality can improve the significance. Experimentally, we observe this phenomenon in a four-photon experiment, testing the Mermin and Ardehali inequality for different levels of noise. Furthermore, we provide a way to develop entanglement tests with high statistical significance.

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arXiv2009

Separability criteria and entanglement witnesses for symmetric quantum states

We study the separability of symmetric bipartite quantum states and show that a single correlation measurement is sufficient to detect the entanglement of any bipartite symmetric state with a non-positive partial transpose. We also discuss entanglement conditions and entanglement witnesses for states with a positive partial transpose.

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arXiv2009

Quantifying entanglement with covariance matrices

Covariance matrices are a useful tool to investigate correlations and entanglement in quantum systems. They are widely used in continuous variable systems, but recently also for finite dimensional systems powerful entanglement criteria in terms of covariance matrices have been derived. We show how these results can be used for the quantification of entanglement in bipartite systems. To that aim we introduce an entanglement parameter that quantifies the violation of the covariance matrix criterion and can be used to give a lower bounds on the concurrence. These lower bounds are easily computable and give entanglement estimates for many weakly entangled states.

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arXiv2009

Entanglement verification with realistic measurement devices via squashing operations

Many protocols and experiments in quantum information science are described in terms of simple measurements on qubits. However, in a real implementation, the exact description is more difficult, and more complicated observables are used. The question arises whether a claim of entanglement in the simplified description still holds, if the difference between the realistic and simplified models is taken into account. We show that a positive entanglement statement remains valid if a certain positive linear map connecting the two descriptions--a so-called squashing operation--exists; then lower bounds on the amount of entanglement are also possible. We apply our results to polarization measurements of photons using only threshold detectors, and derive procedures under which multi-photon events can be neglected.

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arXiv2009

Entanglement and permutational symmetry

We study the separability of permutationally symmetric quantum states. We show that for bipartite symmetric systems most of the relevant entanglement criteria coincide. However, we provide a method to generate examples of bound entangled states in symmetric systems, for the bipartite and the multipartite case. These states shed some new light on the nature of bound entanglement.

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arXiv2009

Spin squeezing and entanglement

What is the relation between spin squeezing and entanglement? To clarify this, we derive the full set of generalized spin squeezing inequalities for the detection of entanglement. These are inequalities for the mean values and variances of the collective angular momentum components J_k. They can be used for the experimental detection of entanglement in a system of spin-1/2 particles in which the spins cannot be individually addressed. We present various sets of inequalities that can detect all entangled states that can be detected based on the knowledge of: (i) the mean values and variances of J_k in three orthogonal directions, or (ii) the variances of J_k in three orthogonal directions, or (iii) the mean values of J_k^2 in three orthogonal directions or (iv) the mean values and variances of J_k in arbitrary directions. We compare our inequalities to known spin squeezing entanglement criteria and discuss to which extent spin squeezing is related to entanglement in the reduced two-qubit states. Finally, we apply our criteria for the detection of entanglement in spin models, showing that they can be used to detect bound entanglement in these systems.

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arXiv2009

Entanglement detection

How can one prove that a given state is entangled? In this paper we review different methods that have been proposed for entanglement detection. We first explain the basic elements of entanglement theory for two or more particles and then entanglement verification procedures such as Bell inequalities, entanglement witnesses, the determination of nonlinear properties of a quantum state via measurements on several copies, and spin squeezing inequalities. An emphasis is given on the theory and application of entanglement witnesses. We also discuss several experiments, where some of the presented methods have been implemented.

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arXiv2008

Demonstrating anyonic fractional statistics with a six-qubit quantum simulator

Anyons are exotic quasiparticles living in two dimensions that do not fit into the usual categories of fermions and bosons, but obey a new form of fractional statistics. Following a recent proposal [Phys. Rev. Lett. 98, 150404 (2007)], we present an experimental demonstration of the fractional statistics of anyons in the Kitaev spin lattice model using a photonic quantum simulator. We dynamically create the ground state and excited states (which are six-qubit graph states) of the Kitaev model Hamiltonian, and implement the anyonic braiding and fusion operations by single-qubit rotations. A phase shift of $π$ related to the anyon braiding is observed, confirming the prediction of the fractional statistics of Abelian 1/2-anyons.

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arXiv2008

Experimental demonstration of a hyper-entangled ten-qubit Schrödinger cat state

Coherent manipulation of an increasing number of qubits for the generation of entangled states has been an important goal and benchmark in the emerging field of quantum information science. The multiparticle entangled states serve as physical resources for measurement-based quantum computing and high-precision quantum metrology. However, their experimental preparation has proved extremely challenging. To date, entangled states up to six, eight atoms, or six photonic qubits have been demonstrated. Here, by exploiting both the photons' polarization and momentum degrees of freedom, we report the creation of hyper-entangled six-, eight-, and ten-qubit Schrödinger cat states. We characterize the cat states by evaluating their fidelities and detecting the presence of genuine multi-partite entanglement. Small modifications of the experimental setup will allow the generation of various graph states up to ten qubits. Our method provides a shortcut to expand the effective Hilbert space, opening up interesting applications such as quantum-enhanced super-resolving phase measurement, graph-state generation for anyonic simulation and topological error correction, and novel tests of nonlocality with hyper-entanglement.

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arXiv2008

Unifying several separability conditions using the covariance matrix criterion

We present a framework for deciding whether a quantum state is separable or entangled using covariance matrices of locally measurable observables. This leads to the covariance matrix criterion as a general separability criterion. We demonstrate that this criterion allows to detect many states where the familiar criterion of the positivity of the partial transpose fails. It turns out that a large number of criteria which have been proposed to complement the positive partial transpose criterion - the computable cross norm or realignment criterion, the criterion based on local uncertainty relations, criteria derived from extensions of the realignment map, and others - are in fact a corollary of the covariance matrix criterion.

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arXiv2008

Generalized Ardehali-Bell inequalities for graph states

We derive Bell inequalities for graph states by generalizing the approach proposed by Ardehali [Phys. Rev. A 46, 5375 (1992)] for Greenberger-Horne-Zeilinger (GHZ) states. Using this method, we demonstrate that Bell inequalities with nonstabilizer observables are often superior to the optimal GHZ-Mermin-type (or stabilizer-type) Bell inequalities.

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arXiv2008

Mermin inequalities for perfect correlations

Any n-qubit state with n independent perfect correlations is equivalent to a graph state. We present the optimal Bell inequalities for perfect correlations and maximal violation for all classes of graph states with n < 7 qubits. Twelve of them were previously unknown and four give the same violation as the Greenberger-Horne-Zeilinger state, although the corresponding states are more resistant to decoherence.

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arXiv2008

Experimental observation of an entire family of four-photon entangled states

A single linear optical set-up is used to observe an entire family of four-photon entangled states. This approach breaks with the inflexibility of present linear-optical set-ups usually designed for the observation of a particular multi-partite entangled state only. The family includes several prominent entangled states that are known to be highly relevant for quantum information applications.

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arXiv2008

Iterations of nonlinear entanglement witnesses

We describe a generic way to improve a given linear entanglement witness by a quadratic, nonlinear term. This method can be iterated, leading to a whole sequence of nonlinear witnesses, which become stronger in each step of the iteration. We show how to optimize this iteration with respect to a given state, and prove that in the limit of the iteration the nonlinear witness detects all states that can be detected by the positive map corresponding to the original linear witness.

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arXiv2008

Optimal spin squeezing inequalities detect bound entanglement in spin models

We determine the complete set of generalized spin squeezing inequalities. These are entanglement criteria that can be used for the experimental detection of entanglement in a system of spin-1/2 particles in which the spins cannot be individually addressed. They can also be used to show the presence of bound entanglement in the thermal states of several spin models.

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