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Geza Toth

Publications and source records attributed to Geza Toth.

At least 55 records · Page 3Linked to original sources
arXiv2010

Number operator-annihilation operator uncertainty as an alternative of the number-phase uncertainty relation

We consider a number operator-annihilation operator uncertainty as a well behaved alternative to the number-phase uncertainty relation, and examine its properties. We find a formulation in which the bound on the product of uncertainties depends on the expectation value of the particle number. Thus, while the bound is not a constant, it is a quantity that can easily be controlled in many systems. The uncertainty relation is approximately saturated by number-phase intelligent states. This allows us to define amplitude squeezing, connecting coherent states to Fock states, without a reference to a phase operator. We propose several setups for an experimental verification.

quant-ph↗
arXiv2010

Generation of macroscopic singlet states in atomic ensembles

We study squeezing of the spin uncertainties by quantum non-demolition (QND) measurement in non-polarized spin ensembles. Unlike the case of polarized ensembles, the QND measurements can be performed with negligible back-action, which allows, in principle, perfect spin squeezing as quantified by [G. Toth et al., Phys. Rev. Lett. 99, 250405 (2007)]. The generated spin states approach many-body singlet states, and contain a macroscopic number of entangled particles, even when individual spin is large. We introduce the Gaussian treatment of unpolarized spin states and use it to estimate the achievable spin squeezing for realistic experimental parameters. Our proposal might have applications for magnetometry with a high spatial resolution or quantum memories storing information in decoherence free subspaces.

quant-ph↗
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.

quant-ph↗
arXiv2009

Graph unique-maximum and conflict-free colorings

We investigate the relationship between two kinds of vertex colorings of graphs: unique-maximum colorings and conflict-free colorings. In a unique-maximum coloring, the colors are ordered, and in every path of the graph the maximum color appears only once. In a conflict-free coloring, in every path of the graph there is a color that appears only once. We also study computational complexity aspects of conflict-free colorings and prove a completeness result. Finally, we improve lower bounds for those chromatic numbers of the grid graph.

cs.DM↗
arXiv2009

Practical methods for witnessing genuine multi-qubit entanglement in the vicinity of symmetric states

We present general numerical methods to construct witness operators for entanglement detection and estimation of the fidelity. Our methods are applied to detecting entanglement in the vicinity of a six-qubit Dicke state with three excitations and also to further entangled symmetric states. All our witnesses are designed to keep the measurement effort small. We present also general results on the efficient local decomposition of permutationally invariant operators, which makes it possible to measure projectors to symmetric states efficiently

quant-ph↗
arXiv2009

Experimental entanglement of a six-photon symmetric Dicke state

We report on the experimental observation and characterization of a six-photon entangled Dicke state. We obtain a fidelity as high as 0.654$\pm$0.024 and prove genuine six-photon entanglement by, amongst others, a two-setting witness yielding -0.422$\pm$0.148. This state has remarkable properties; e.g., it allows obtaining inequivalent entangled states of a lower qubit number via projective measurements, and it possesses a high entanglement persistency against qubit loss. We characterize the properties of the six-photon Dicke state experimentally by detecting and analyzing the entanglement of a variety of multipartite entangled states.

quant-ph↗
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.

quant-ph↗
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.

quant-ph↗
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.

quant-ph↗
arXiv2008

QUBIT4MATLAB V3.0: A program package for quantum information science and quantum optics for MATLAB

A program package for MATLAB is introduced that helps calculations in quantum information science and quantum optics. It has commands for the following operations: (i) Reordering the qudits of a quantum register, computing the reduced state of a quantum register. (ii) Defining important quantum states easily. (iii) Formatted input and output for quantum states and operators. (iv) Constructing operators acting on given qudits of a quantum register and constructing spin chain Hamiltonians. (v) Partial transposition, matrix realignment and other operations related to the detection of quantum entanglement. (vi) Generating random state vectors, random density matrices and random unitaries.

quant-ph↗
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.

quant-ph↗
arXiv2007

Noise robustness of the nonlocality of entangled quantum states

We study the nonlocal properties of states resulting from the mixture of an arbitrary entangled state rho of two d-dimensional systems and completely depolarized noise, with respective weights p and 1-p. We first construct a local model for the case in which rho is maximally entangled and p at or below a certain bound. We then extend the model to arbitrary rho. Our results provide bounds on the resistance to noise of the nonlocal correlations of entangled states. For projective measurements, the critical value of the noise parameter p for which the state becomes local is at least asymptotically log(d) larger than the critical value for separability.

quant-ph↗
arXiv2007

Efficient algorithm for multi-qudit twirling for ensemble quantum computation

We present an efficient algorithm for twirling a multi-qudit quantum state. The algorithm can be used for approximating the twirling operation in an ensemble of physical systems in which the systems cannot be individually accessed. It can also be used for computing the twirled density matrix on a classical computer. The method is based on a simple non-unitary operation involving a random unitary. When applying this basic building block iteratively, the mean squared error of the approximation decays exponentially. In contrast, when averaging over random unitary matrices the error decreases only algebraically. We present evidence that the unitaries in our algorithm can come from a very imperfect random source or can even be chosen deterministically from a set of cyclically alternating matrices. Based on these ideas we present a quantum circuit realizing twirling efficiently.

quant-ph↗
arXiv2007

Detection of multipartite entanglement in the vicinity of symmetric Dicke states

We present methods for detecting entanglement around symmetric Dicke states. In particular, we consider N-qubit symmetric Dicke states with N/2 excitations. In the first part of the paper we show that for large N these states have the smallest overlap possible with states without genuine multi-partite entanglement. Thus these states are particulary well suited for the experimental examination of multi-partite entanglement. We present fidelity-based entanglement witness operators for detecting multipartite entanglement around these states. In the second part of the paper we consider entanglement criteria, somewhat similar to the spin squeezing criterion, based on the moments or variances of the collective spin operators. Surprisingly, these criteria are based on an upper bound for variances for separable states. We present both criteria detecting entanglement in general and criteria detecting only genuine multi-partite entanglement. The collective operator measured for our criteria is an important physical quantity: Its expectation value essentially gives the intensity of the radiation when a coherent atomic cloud emits light.

quant-ph↗
arXiv2006

Genuine three-partite entangled states with a local hidden variable model

We present a family of three-qubit quantum states with a basic local hidden variable model. Any von Neumann measurement can be described by a local model for these states. We show that some of these states are genuine three-partite entangled and also distillable. The generalization for larger dimensions or higher number of parties is also discussed. As a byproduct, we present symmetric extensions of two-qubit Werner states.

quant-ph↗
arXiv2006

Experimental Observation of Four-Photon Entangled Dicke State with High Fidelity

We present the experimental observation of the symmetric four-photon entangled Dicke state with two excitations $|D_{4}^{(2)}>$. A simple experimental set-up allowed quantum state tomography yielding a fidelity as high as $0.844 \pm 0.008$. We study the entanglement persistency of the state using novel witness operators and focus on the demonstration of a remarkable property: depending on the orientation of a measurement on one photon, the remaining three photons are projected into both inequivalent classes of genuine tripartite entanglement, the GHZ and W class. Furthermore, we discuss possible applications of $|D_{4}^{(2)}>$ in quantum communication.

quant-ph↗
arXiv2006

Two-setting Bell Inequalities for Graph States

We present Bell inequalities for graph states with high violation of local realism. In particular, we show that there is a two-setting Bell inequality for every nontrivial graph state which is violated by the state at least by a factor of two. These inequalities are facets of the convex polytope containing the many-body correlations consistent with local hidden variable models. We first present a method which assigns a Bell inequality for each graph vertex. Then for some families of graph states composite Bell inequalities can be constructed with a violation of local realism increasing exponentially with the number of qubits. We also suggest a systematic way for obtaining Bell inequalities with a high violation of local realism for arbitrary graphs.

quant-ph↗