Showing papers on "Concurrence published in 2009"

Tripartite entanglement witnesses and entanglement sudden death

Abstract: I explore entanglement dynamics in a three qubit system comparing the ability of entanglement witnesses to detect tripartite entanglement to the phenomenon of entanglement sudden death (ESD). Using a system subject to dephasing I invoke entanglement witnesses to detect tripartite Greenberger-Horne-Zeilinger (GHZ)-type and $W$-type entanglement and compare the evolution of their detection capabilities with the evolution of the negativity, bipartite concurrence, and tripartite negativity. Interestingly, I find a state in which there is no concurrence or tripartite negativity but there is entanglement. Finally, I utilize a three qubit quantum error correction code to address how ESD affects the abilities of quantum error correction.

A lower bound of concurrence for multipartite quantum states

Abstract: We study the concurrence of arbitrary multipartite mixed quantum states. An explicit lower bound of the concurrence is derived, which detects quantum entanglement of some states better than some separability criteria, and gives sufficient conditions for distilling GHZ states from tripartite states. An interesting relation between the lower bound of the concurrence for bipartite states and for tripartite states has been presented.

Decoherence effects in interacting qubits under the influence of various environments

Abstract: We study competition between the dissipative and coherent effects in the entanglement dynamics of two qubits. The coherent interactions are needed for designing logic gate operations with systems such as ion traps, semiconductor quantum dots and atoms. We show that the interactions lead to a phenomenon of periodic disentanglement and entanglement between the qubits. The disentanglement is primarily caused by environmental perturbations. The qubits are seen to remain disentangled for a finite time before getting entangled again. We find that the phenomenon is generic and occurs for a wide variety of models of the environment. We present analytical results for the time dependence of concurrence for all the models. The periodic disentanglement and entanglement behaviour is seen to be a precursor to the sudden death of entanglement (ESD) and can happen for environments which do not show ESD for non-interacting qubits. Further we also find that this phenomenon can even lead to delayed death of entanglement for correlated environments.

Non-Markovian entanglement dynamics between two coupled qubits in the same environment

Abstract: We analyze the dynamics of the entanglement in two independent non-Markovian channels. In particular, we focus on the entanglement dynamics as a function of the initial states and the channel parameters, such as the temperature and the ratio r between ?0, the characteristic frequency of the quantum system of interest, and ?c, the cut-off frequency of the Ohmic reservoir. We give a stationary analysis of the concurrence and find that the dynamic of non-Markovian entanglement concurrence at temperature kBT = 0 is different from the kBT > 0 case. We find that 'entanglement sudden death' (ESD) depends on the initial state when kBT = 0, otherwise the concurrence always disappears at a finite time when kBT > 0, which means that the ESD must happen. The main result of this paper is that the non-Markovian entanglement dynamic is fundamentally different from the Markovian one. In the Markovian channel, entanglement decays exponentially and vanishes only asymptotically, but in the non-Markovian channel the concurrence oscillates, especially in the high temperature case. Then an open-loop controller adjusted by the temperature is proposed to control the entanglement and prolong the ESD time.

Necessary conditions for entanglement catalysts

Abstract: Given a pure state transformation $\ensuremath{\psi}\ensuremath{\mapsto}\ensuremath{\phi}$ restricted to entanglement-assisted local operations with classical communication, we determine a lower bound for the dimension of a catalyst allowing that transformation. Our bound is stated in terms of the generalized concurrence monotones (the usual concurrence of two qubits is one such monotone). We further provide tools for deriving further conditions upon catalysts of pure state transformations.

Sudden death and birth of entanglement effects for Kerr-nonlinear coupler

Abstract: We analyze the entanglement dynamics in a nonlinear Kerr-like coupler interacting with external environment. Whenever the reservoir is in a thermal vacuum state, the entanglement (measured by concurrence for a two-qubit system) exhibits regular oscillations of decreasing amplitude. In contrast, for thermal reservoirs we can observe dark periods in concurrence oscillations (which can be called a sudden death of the entanglement) and the entanglement rebuild (which can be named the sudden birth of entanglement). We show that these features can be observed when we deal with two-qubit system as well as qubit-qutrit system.

The entanglement dynamics of the bipartite quantum system: toward entanglement sudden death

Abstract: We investigate the entanglement dynamics of the bipartite quantum system between two qubits with the dissipative environment. We begin with the standard Markovian master equation in the Lindblad form and the initial state which is prepared in the extended Werner-like state: ρΦAB(0). We examine the conditions for entanglement sudden death (ESD) and calculate the corresponding ESD time by the Wootters concurrence. We observe that ESD is determined by the parameters such as the mean occupation number of the environment N, amount of initial entanglement α and the purity r. For N = 0, we get the analytical expressions of both ESD condition and ESD time. For N > 0 we give a theoretical analysis that ESD always occurs, and simulate the concurrence as a function of γ0t and one of the parameters N, α and r.

Entanglement in a three-qubit anisotropic Heisenberg XXZ spin ring with Dzyaloshinskii–Moriya interaction

Abstract: We investigate the entanglement of a three-qubit anisotropic Heisenberg XXZ ring with Dzyaloshinskii–Moriya (DM) interaction in thermal equilibrium at temperature T in the presence of an external magnetic field B along the z-axis and obtain analytic expression for the concurrence, in which the dependence of the concurrence on the anisotropic coupling coefficient Jz, external magnetic field B, the DM interaction parameter D and temperature T is described. The DM interaction is found to have a more significant role than the others in increasing the critical temperature or the entanglement area. We also calculate the ground-state entanglement under various control parameters and give expressions for the quantum critical points at which quantum phase transition (QPT) takes place. These results show that one is able to produce, when it does not exist, or increase (up to some limit), when it exists, the concurrence so that the efficient control of entanglement by appropriate combinations of the tunable parameters may be possible.

Towards measurable bounds on entanglement measures

Abstract: While the experimental detection of entanglement provides already quite a difficult task, experimental quantification of entanglement is even more challenging, and has not yet been studied thoroughly. In this paper we discuss several issues concerning bounds on concurrence measurable collectively on copies of a given quantum state. Firstly, we concentrate on the recent bound on concurrence by (Mintert and Buchleitner in Phys Rev Lett 98:140505/1---140505/4, 2007). Relating it to the reduction criterion for separability we provide yet another proof of the bound and point out some possibilities following from the proof which could lead to improvement of the bound. Then, relating concurrence to the generalized robustness of entanglement, we provide a method allowing for construction of lower bounds on concurrence from any positive map (not only the reduction one). All these quantities can be measured as mean values of some two-copy observables. In this sense the method generalizes the Mintert---Buchleitner bound and recovers it when the reduction map is used. As a particular case we investigate the bound obtained from the transposition map. Interestingly, comparison with MB bound performed on the class of $${4\otimes 4}$$ rotationally invariant states shows that the new bound is positive in regions in which the MB bound gives zero. Finally, we provide measurable upper bounds on the whole class of concurrences.

Direct measurements of entanglement and permutation symmetry

Abstract: So-called direct measurements of entanglement are collective measurements on multiple copies of a (bipartite or multipartite) quantum system that directly provide one with a value for some entanglement measure, such as the concurrence for bipartite states. Multiple copies are needed since the entanglement of a mixed state is not a linear function of the density matrix. The procedures proposed and implemented so far make certain assumptions about the states generated. This feature distinguishes direct measurements from standard entanglement verification tests such as Bell inequalities, entanglement witnesses, and quantum-state tomography, which make no such assumptions. I discuss how a direct measurement can be turned into a quantitative entanglement verification test without such assumptions by exploiting a recent theorem by Renner [Nature Phys. 3, 645 (2007)].

Entanglement Metrology Using a Joint Readout of Superconducting Qubits

Abstract: Accurate and precise detection of multi-qubit entanglement is key for the experimental development of quantum computation. Traditionally, non-classical correlations between entangled qubits are measured by counting coincidences between single-shot readouts of individual qubits. We report entanglement metrology using a single detection channel with direct access to ensemble-averaged correlations between two superconducting qubits. Following validation and calibration of this joint readout, we demonstrate full quantum tomography on both separable and highly-entangled two-qubit states produced on demand. Using a subset of the measurements required for full tomography, we perform entanglement metrology with ~95% accuracy and ~98% precision despite ~10% fidelity of single measurements. For the highly entangled states, measured Clauser-Horne-Shimony-Holt operators reach a maximum value of 2.61+/-0.04 and entanglement witnesses give a lower bound of ~88% on concurrence. In its present form, this detector will be able to resolve future improvements in the production of two-qubit entanglement and is immediately extendable to 3 or 4 qubits.

Entanglement optimizing mixtures of two-qubit states

Abstract: Entanglement in incoherent mixtures of pure states of two qubits is considered via the concurrence measure. A set of pure states is optimal if the concurrence for any mixture of them is the weighted sum of the concurrences of the generating states. When two or three pure real states are mixed it is shown that 28.5% and 5.12% of the cases respectively, are optimal. Conditions that are obeyed by the pure states generating such optimally entangled mixtures are derived. For four or more pure states it is shown that there are no such sets of real states. The implications of these on superposition of two or more dimerized states is discussed. A corollary of these results also show in how many cases rebit concurrence can be the same as that of qubit concurrence.

Genuine tripartite entanglement in quantum brachistochrone evolution of a three-qubit system

Abstract: We explore the connection between quantum brachistochrone (time-optimal) evolution of a three-qubit system and its residual entanglement called three-tangle. The result shows that the entanglement between two qubits is not required for some brachistochrone evolutions of a three-qubit system. However, the evolution between two distinct states cannot be implemented without its three-tangle, except for the trivial cases in which less than three qubits attend evolution. Although both the probability density function of the time-averaged three-tangle and that of the time-averaged squared concurrence between two subsystems become more and more uniform with the decrease in angles of separation between an initial state and a final state, the features of their most probable values exhibit a different trend.

Experimental measurement of lower and upper bounds of concurrence for mixed quantum states

Abstract: We experimentally measure the lower and upper bounds of concurrence for a set of two-qubit mixed quantum states using photonic systems. The measured concurrence bounds are in agreement with the results evaluated from the density matrices reconstructed through quantum state tomography. In our experiment, we propose and demonstrate a simple method for providing two faithful copies of a two-photon mixed state required for parity measurements: two photon pairs generated by two neighboring pump-laser pulses through optical parametric down-conversion processes represent two identical copies. This method can be conveniently generalized for entanglement estimation of multiphoton mixed states.

Typical features of the Mintert-Buchleitner lower bound for concurrence

Abstract: This work was partially supported by MEC Grant No. FIS2008-00781 Spain, EU , by Junta de Andalucia Programs No. FQM-2445 and No. FQM-207 Spain, EU , by FEDER EU , and by CONICET Argentine Agency . A.B. and A.P.M. acknowledge support from MEC through FPU Grant No. AP-2004-962 and Contract No. SB-2006-0165.

Towards measurable bounds on entanglement measures

Abstract: While the experimental detection of entanglement provides already quite a difficult task, experimental quantification of entanglement is even more challenging, and has not yet been studied thoroughly. In this paper we discuss several issues concerning bounds on concurrence measurable collectively on copies of a given quantum state. Firstly, we concentrate on the recent bound on concurrence by Mintert--Buchleitner [F. Mintert and A. Buchleitner, Phys. Rev. Lett. 98, 140505 (2007)]. Relating it to the reduction criterion for separability we provide yet another proof of the bound and point out some possibilities following from the proof which could lead to improvement of the bound. Then, relating concurrence to the generalized robustness of entanglement, we provide a method allowing for construction of lower bounds on concurrence from any positive map (not only the reduction one). All these quantities can be measured as mean values of some two--copy observables. In this sense the method generalizes the Mintert--Buchleitner bound and recovers it when the reduction map is used. As a particular case we investigate the bound obtained from the transposition map. Interestingly, comparison with MB bound performed on the class of 4\otimes 4 rotationally invariant states shows that the new bound is positive in regions in which the MB bound gives zero. Finally, we provide measurable upper bounds on the whole class of concurrences.

Application of quantum algorithms to direct measurement of concurrence of a two-qubit pure state ⁄

Abstract: This paper proposes a method to measure directly the concurrence of an arbitrary two-qubit pure state based on a generalized Grover quantum iteration algorithm and a phase estimation algorithm. The concurrence can be calculated by applying quantum algorithms to two available copies of the bipartite system, and a final measurement on the auxiliary working qubits gives a better estimation of the concurrence. This method opens new prospects of entanglement measure by the application of quantum algorithms. The implementation of the protocol would be an important step toward quantum information processing and more complex entanglement measure of the finite-dimensional quantum system with an arbitrary number of qubits.

A Lower Bound on Concurrence

Abstract: We derive an analytical lower bound on the concurrence for bipartite quantum systems with an improved computable cross norm or realignment criterion and an improved positive partial transpose criterion respectively. Furthermore we demonstrate that our bound is better than that obtained from the local uncertainty relations criterion with optimal local orthogonal observables which is known as one of the best estimations of concurrence.

Concurrence and entanglement entropy of stochastic one-qubit maps

Abstract: Explicit expressions for the concurrence of all positive and trace-preserving (``stochastic'') one-qubit maps are presented. Our method allows to construct the relevant convex roof patterns. We conclude that two-component optimal decompositions always exist. Our results can be transferred to $2\ifmmode\times\else\texttimes\fi{}n$-quantum systems providing the concurrence for all rank-two density operators, as well as lower and upper bounds for their entanglement of formation. We apply these results to a study of the entanglement entropy of one-qubit stochastic maps which preserve axial symmetry. Using analytic and numeric results we analyze the bifurcation patterns appearing in the convex roof of optimal decompositions and give results for the one-shot (Holevo-Schumacher-Westmoreland) capacity of those maps.

Competition, autonomy and new thinking: Transformation of higher education in Federal Germany

Abstract: Germany has recently gone through a fundamental process of reform of its higher education system. The last 15 years have been characterised by significant changes in virtually all aspects of the system. The impacts of the Bologna Process have been far reaching. The reform of the governance and funding systems in higher education has also been highly influential. This article reflects upon the increasing relevance of the concept of competition in higher education and how the realisation of more competitive elements was accomplished in a highly decentralised system of governance. The article also demonstrates the complex interplay between the public discourse regarding the need for more competitive approaches in higher education, legal reforms, changes in funding provisions for higher education and the transformation of rules for attracting human resources. Concurrence, autonomie et nouveau courant de pensee : transformation de l’enseignement superieur en Allemagne federaleLe systeme de l’enseignement superieur allemand a recemment connu un processus de reformes fondamental. Ces 15 dernieres annees ont ete marquees par des changements importants affectant quasiment tous les aspects du systeme. Les impacts du processus de Bologne ont ete considerables. De la meme maniere, la reforme des systemes de gouvernance et de financement dans l’enseignement superieur a exerce une grande influence. Cet article analyse l’interet croissant accorde a la notion de concurrence dans l’enseignement superieur et la facon dont des elements plus competitifs ont ete mis en place dans un systeme de gouvernance fortement decentralise. L’article demontre l’existence d’interactions complexes entre le discours public sur les besoins d’une approche plus concurrentielle dans l’enseignement superieur, les reformes legales, les changements apportes a l’attribution de financement et la transformation des regles visant a attirer les ressources humaines.

Pairwise entanglement and geometric phase in high dimensional free-Fermion lattice systems

Abstract: The pairwise entanglement, measured by concurrence and geometric phase in high dimensional free-Fermion lattice systems have been studied in this paper. When the system stays at the ground state, their derivatives with the external parameter show the singularity closed to the phase transition points, and can be used to detect the phase transition in this model. Furthermore our studies show for the free-Fermion model that both concurrence and geometric phase show the intimate connection with the correlation functions. The possible connection between concurrence and geometric phase has been also discussed.

Delayed sudden birth and sudden death of entanglement in Josephson-charge qubits

Abstract: Distinctive features of the entanglement dynamics of a circuit containing two-coupled superconducting charge qubits are explored. The striking effects of junction coupling on the entanglement are presented in terms of the concurrence. We also point out the importance effects of initial state selection for obtaining different features of entanglement, such as, sudden death and sudden birth.

Entanglement patterns and pure quantum correlations in the Heisenberg X Y model

Abstract: We investigate the possibility of the existence of different types of thermal entanglement in the two-spin Heisenberg $XY$ model, which are distinguished by the behavior of the concurrence as a function of the model parameters. Singularities in the temperature threshold for thermal entanglement and in the ground-state energy as a function of the model parameters are used to construct diagrams containing boundary lines separating the several types of thermal entanglement in the system, showing an unexpected rich structure. We discuss a procedure to extract a pure quantum component from the spin-correlation function at arbitrary temperatures, by using the explicit form of the decomposition that minimizes the concurrence, and show that it is highly sensitive to the different patterns of thermal entanglement.

Measurable lower bounds on concurrence

Abstract: We derive measurable lower bounds on concurrence of arbitrary mixed states, for both bipartite and multipartite cases. First, we construct measurable lower bonds on the purely algebraic bounds of concurrence [F. Mintert et al. (2004), Phys. Rev. lett., 92, 167902]. Then, using the fact that the sum of the square of the algebraic bounds is a lower bound of the squared concurrence, we sum over our measurable bounds to achieve a measurable lower bound on concurrence. With two typical examples, we show that our method can detect more entangled states and also can give sharper lower bonds than the similar ones.

Optically pumping hole spins in coupled quantum dot molecules into a steady state of high concurrence entanglement

Abstract: We present a way to prepare a high concurrence steady state entanglement of two hole spins in a quantum dot molecule. We show that the spontaneous dissipation can be used to induce and stabilize the entanglement with rapid rate. By optical pumping of trion levels, two-qubit singlet state can be automatically generated. We also show that our proposal can synchronously accomplish both initialization and entanglement generation. The effects of acoustic phonons and electron tunneling are also discussed and we find that the main influence is from deformation potential coupling to acoustic phonons in InAs/GaAs quantum dots. At low temperature, we show that concurrence of entanglement can be greater than 0.95 at $T=1\text{ }\text{K}$.

Les politiques de concurrence européenne et américaine face aux remises de fidélité accordées par une entreprise dominante : L'affaire Intel

Abstract: The European Commission has imposed, the 13th May 2009, a huge fine of €1.06 bn on Intel for abuses of dominant position. According to the European Commission, throughout the period October 2002-December 2007, Intel engaged illegal practices to exclude its rival AMD from the market of computer chips. The case puts into relief the issue of the possibility for a dominant firm to implement fidelity rebates, without distorting competition. Such practices are commonly assessed very differently on the both side of Atlantic. When European competition policy remains inspired by the Freiburg School of Law and Economics, the US one is shaped by the Chicago’s approach. The purpose of this article is to put the present case into the perspective of competition economics. We also aim at discussing on the potential reconciliation of these two perspectives in a context of a reassessment of the antitrust treatment of dominant firms’ unilateral practices in the United States and of a European willingness to promote a more economic approach of the EC article 82 enforcement. La condamnation d’Intel par la Commission europeenne a une amende de plus d’un milliard d’euros le 13 mai 2009 vient sanctionner un ensemble de pratiques jugees par cette derniere contraires aux regles de concurrence. Dans sa lutte contre le fabricant de microprocesseurs Advanced Micro Devices (AMD) dont la part de marche mondiale s’etablit a 19 %, Intel, operateur tres largement dominant avec une part de marche de 80 %, s’est rendue coupable, aux yeux de la Commission d’avoir mis en œuvre un certain nombre de pratiques anticoncurrentielles. Celles-ci tiennent en des remises de fidelite accordees a certains constructeurs de PC afin de nouer une relation (quasi) exclusive avec ces derniers, en des ventes de processeurs a des prix inferieurs a leurs couts mais aussi en des paiements directs en faveur de certains d’entre eux pour qu’ils entravent la sortie de PC equipes de puces AMD. Outre la gravite des pratiques imputees a Intel et le montant eleve de la sanction pecuniaire, l’un des points les plus interessants a relever dans cette affaire tient au fait qu’Intel a ete poursuivie et condamnee pour les memes raisons par les autorites de la concurrence

Heralded Entanglement of Arbitrary Degree in Remote Qubits

Abstract: Incoherent scattering of photons off two remote atoms with a Lambda-level structure is used as a basic Young-type interferometer to herald long-lived entanglement of an arbitrary degree. The degree of entanglement, as measured by the concurrence, is found to be tunable by two easily accessible experimental parameters. Fixing one of them to certain values unveils an analog to the Malus' law. An estimate of the variation in the degree of entanglement due to uncertainties in an experimental realization is given.

Decoherence effects in interacting qubits under the influence of various environments

Abstract: We study competition between the dissipative and coherent effects in the entanglement dynamics of two qubits. The coherent interactions are needed for designing logic gate operations with systems like ion traps, semicondutor quantum dots and atoms. We show that the interactions lead to a phenomenon of periodic disentanglement and entanglement between the qubits. The disentanglement is primarily caused by environmental perturbations. The qubits are seen to remain disentangled for a finite time before getting entangled again. We find that the phenomenon is generic and occurs for wide variety of models of the environment. We present analytical results for the time dependence of concurrence for all the models. The periodic disentanglement and entanglement behavior is seen to be precursor to the sudden death of entanglement (ESD) and can happen, for environments which do not show ESD for noninteracting qubits. Further we also find that this phenomenon can even lead to delayed death of entanglement for correlated environments.