arXiv subjects

Geza Toth

Publications and source records attributed to Geza Toth.

At least 73 records · Page 4Linked to original sources

arXiv2006

Energy and multipartite entanglement in multidimensional and frustrated spin models

We investigate the relation between the entanglement properties of a quantum state and its energy for macroscopic spin models. To this aim, we develop a general method to compute energy bounds for states without certain forms of multipartite entanglement. Violation of these bounds implies the presence of these types of multipartite entanglement. As examples, we investigate the Heisenberg model in different dimensions, the Ising model and the XX model in the presence of a magnetic field. Finally, by studying the Heisenberg model on a triangular lattice, we demonstrate that our techniques can be applied also to frustrated systems.

quant-ph↗

arXiv2006

Detection of multipartite entanglement with two-body correlations

We show how to detect entanglement with criteria built from simple two-body correlation terms. Since many natural Hamiltonians are sums of such correlation terms, our ideas can be used to detect entanglement by energy measurement. Our criteria can straightforwardly be applied for detecting different forms of multipartite entanglement in familiar spin models in thermal equilibrium.

quant-ph↗

arXiv2005

Multipartite entanglement in spin chains

We investigate the presence of multipartite entanglement in macroscopic spin chains. We discuss the Heisenberg and the XY model and derive bounds on the internal energy for systems without multipartite entanglement. Based on this we show that in thermal equilibrium the above mentioned spin systems contain genuine multipartite entanglement, even at finite modest temperatures.

quant-ph↗

arXiv2005

Experimental Analysis of a 4-Qubit Cluster State

Linear optics quantum logic operations enabled the observation of a four-photon cluster state. We prove genuine four-partite entanglement and study its persistency, demonstrating remarkable differences to the usual GHZ state. Efficient analysis tools are introduced in the experiment, which will be of great importance in further studies on multi-particle entangled states.

quant-ph↗

arXiv2005

Bell Inequalities for Graph States

We investigate the non-local properties of graph states. To this aim, we derive a family of Bell inequalities which require three measurement settings for each party and are maximally violated by graph states. In turn, for each graph state there is an inequality maximally violated only by that state. We show that for certain types of graph states the violation of these inequalities increases exponentially with the number of qubits. We also discuss connections to other entanglement properties such as the positivity of the partial transpose or the geometric measure of entanglement.

quant-ph↗

arXiv2005

Addendum to "Sufficient conditions for three-particle entanglement and their tests in recent experiments"

A recent paper [M. Seevinck and J. Uffink, Phys. Rev. A 65, 012107 (2002)] presented a bound for the three-qubit Mermin inequality such that the violation of this bound indicates genuine three-qubit entanglement. We show that this bound can be improved for a specific choice of observables. In particular, if spin observables corresponding to orthogonal directions are measured at the qubits (e.g., X and Y spin coordinates) then the bound is the same as the bound for states with a local hidden variable model. As a consequence, it can straightforwardly be shown that in the experiment described by J.-W. Pan et al. [Nature 403, 515 (2000)] genuine three-qubit entanglement was detected.

quant-ph↗

arXiv2005

Entanglement Detection in the Stabilizer Formalism

We investigate how stabilizer theory can be used for constructing sufficient conditions for entanglement. First, we show how entanglement witnesses can be derived for a given state, provided some stabilizing operators of the state are known. These witnesses require only a small effort for an experimental implementation and are robust against noise. Second, we demonstrate that also nonlinear criteria based on uncertainty relations can be derived from stabilizing operators. These criteria can sometimes improve the witnesses by adding nonlinear correction terms. All our criteria detect states close to Greenberger-Horne-Zeilinger states, cluster and graph states. We show that similar ideas can be used to derive entanglement conditions for states which do not fit the stabilizer formalism, such as the three-qubit W state. We also discuss connections between the witnesses and some Bell inequalities.

quant-ph↗

arXiv2005

Detecting Genuine Multipartite Entanglement with Two Local Measurements

We present entanglement witness operators for detecting genuine multipartite entanglement. These witnesses are robust against noise and require only two local measurement settings when used in an experiment, independent from the number of qubits. This allows detection of entanglement for an increasing number of parties without a corresponding increase in effort. The witnesses presented detect states close to GHZ, cluster and graph states. Connections to Bell inequalities are also discussed.

quant-ph↗

arXiv2004

Two measurement settings can suffice to verify multipartite entanglement

We present entanglement witnesses for detecting genuine multi-qubit entanglement. Our constructions are robust against noise and require only two local measurement settings, independent of the number of qubits. Thus they allow to verify entanglement of many qubits in experiments while requiring only a small effort. In contrast, usual methods need an effort which increases exponentially with the number of qubits. The witnesses detect states close to GHZ states and cluster states.

quant-ph↗

arXiv2004

Entanglement Detection in Optical Lattices of Bosonic Atoms with Collective Measurements

The minimum requirements for entanglement detection are discussed for a spin chain in which the spins cannot be individually accessed. The methods presented detect entangled states close to a cluster state and a many-body singlet state, and seem to be viable for experimental realization in optical lattices of two-state bosonic atoms. The entanglement criteria are based on entanglement witnesses and on the uncertainty of collective observables.

quant-ph↗

arXiv2003

Entanglement Detection Based on Interference and Particle Counting

A sufficient condition for entanglement in two-mode continuous systems is constructed based on interference visibility and the uncertainty of the total particle number. The observables to be measured (particle numbers and particle number variances) are relatively easily accessible experimentally. The method may be used to detect entanglement in light fields or in Bose-Einstein condensates. In contrast to the standard approach based on entanglement witnesses, the condition is expressed in terms of an inequality which is nonlinear in expectation values.

quant-ph↗

arXiv2003

Hydrodynamics of domain growth in nematic liquid crystals

We study the growth of aligned domains in nematic liquid crystals. Results are obtained solving the Beris-Edwards equations of motion using the lattice Boltzmann approach. Spatial anisotropy in the domain growth is shown to be a consequence of the flow induced by the changing order parameter field (backflow). The generalization of the results to the growth of a cylindrical domain, which involves the dynamics of a defect ring, is discussed.

cond-mat.soft↗

arXiv2002

Modelling nematohydrodynamics in liquid crystal devices

We formulate a lattice Boltzmann algorithm which solves the hydrodynamic equations of motion for nematic liquid crystals. The applicability of the approach is demonstrated by presenting results for two liquid crystal devices where flow has an important role to play in the switching.

cond-mat.soft↗

arXiv2002

Domain motion in confined liquid crystals

We extend a lattice Boltzmann algorithm of liquid crystal hydrodynamics to include an applied electric field. The approach solves the equations of motion written in terms of a tensor order parameter. Back-flow effects and the hydrodynamics of topological defects are included. We investigate some of the dynamics relevant to liquid crystal devices; in particular defect-mediated motion of domain walls relevant to the nucleation of states useful in pi-cells. An anisotropy in the domain wall velocity is seen because defects of different topology couple differently to the flow field.

cond-mat.soft↗

arXiv2002

Hydrodynamics of topological defects in nematic liquid crystals

We show that back-flow, the coupling between the order parameter and the velocity fields, has a significant effect on the motion of defects in nematic liquid crystals. In particular the defect speed can depend strongly on the topological strength in two dimensions and on the sense of rotation of the director about the core in three dimensions.

cond-mat.soft↗

arXiv2001

The Role of Correlation in the Operation of Quantum-dot Cellular Automata

Quantum-dot Cellular Automata (QCA) may offer a viable alternative of traditional transistor-based technology at the nanoscale. When modeling a QCA circuit, the number of degrees of freedom necessary to describe the quantum mechanical state increases exponentially making modeling even modest size cell arrays difficult. The intercellular Hartree approximation largely reduces the number of state variables and still gives good results especially when the system remains near ground state. This suggests that large part of the correlation degrees of freedom are not essential from the point of view of the dynamics. In certain cases, however, such as for example the majority gate with unequal input legs, the Hartree approximation gives qualitatively wrong results. An intermediate model is constructed between the Hartree approximation and the exact model, based on the coherence vector formalism. By including correlation effects to a desired degree, it improves the results of the Hartree method and gives the approximate dynamics of the correlation terms. It also models the majority gate correctly. Beside QCA cell arrays, our findings are valid for Ising spin chains in transverse magnetic field, and can be straightforwardly generalized for coupled two-level systems with a more complicated Hamiltonian.

cond-mat.mes-hall↗

arXiv2000

Quantum Cellular Neural Networks

We have previously proposed a way of using coupled quantum dots to construct digital computing elements - quantum-dot cellular automata (QCA). Here we consider a different approach to using coupled quantum-dot cells in an architecture which, rather that reproducing Boolean logic, uses a physical near-neighbor connectivity to construct an analog Cellular Neural Network (CNN).

cond-mat.mes-hall↗

arXiv2000

Quasi-adiabatic Switching for Metal-Island Quantum-dot Cellular Automata

Recent experiments have demonstrated a working cell suitable for implementing the Quantum-dot Cellular Automata (QCA) paradigm. These experiments have been performed using metal island clusters. The most promising approach to QCA operation involves quasi-adiabatically switching the cells. This has been analyzed extensively in gated semiconductor cells. Here we present a metal island cell structure that makes quasi-adiabatic switching possible. We show how this permits quasi-adiabatic clocking, and enables a pipelined architecture.

cond-mat.mes-hall↗