An entanglement criterion for states in infinite-dimensional multipartite quantum systems

Wang, Yinzhu; Hou, Jinchuan; Guo, Yu

doi:10.1007/s11434-012-5111-5

Chin. Sci. Bull.

2012

DOI: 10.1007/s11434-012-5111-5

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An entanglement criterion for states in infinite-dimensional multipartite quantum systems

Yinzhu Wang

Jinchuan Hou

Yu Guo

Abstract: In (Phys Lett A, 2002, 297: 4-8) an entanglement criterion for finite-dimensional bipartite systems is proposed: If ρ AB is a separable state, then Tr(ρ 2 A ) Tr(ρ 2 ) and Tr(ρ 2 B ) Tr(ρ 2 ). In the present paper this criterion is extended to infinite-dimensional bipartite and multipartite systems. The reduction criterion presented in (Phys Rev A, 1999, 59: 4206-4216) is also generalized to infinitedimensional case. Then it is shown that the former criterion is weaker than the later one. quantum state, enta… Show more

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Cited by 11 publications

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“…Quantum entanglement led to the experimental verification for Bell inequality which confirmed quantum mechanics [3]. In recent years, quantum entanglement has been one of the key driving forces that advanced the explosive development of quantum information and quantum computation [4][5][6][7][8][9][10][11][12]. Entanglement has developed from a philosophical concept into a frontier research paradigm, and much more attention has been paid to the quantification of entanglement.…”

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confidence: 99%

Entanglement of linear cluster states in terms of averaged entropies

Cao

Long

2013

Chin. Sci. Bull.

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An entanglement measure, multiple entropy measures (MEMS) was proposed recently by using the geometric mean of partial entropies over all possible i-body combinations of the quantum system. In this work, we study the average subsystem von Neumann entropies of the linear cluster state and investigated the quantum entanglement of linear cluster states in terms of MEMS. Explicit results with specific particle numbers are calculated, and some analytical results are given for systems with arbitrary particle numbers. Compared with other example quantum states such as the GHZ states and W states, the linear cluster states are "more entangled" in terms of MEMS, namely their averaged entropies are larger than the GHZ states and W states. Entanglement [1, 2] is one of the most salient properties of quantum systems. Quantum entanglement led to the experimental verification for Bell inequality which confirmed quantum mechanics [3]. In recent years, quantum entanglement has been one of the key driving forces that advanced the explosive development of quantum information and quantum computation [4][5][6][7][8][9][10][11][12]. Entanglement has developed from a philosophical concept into a frontier research paradigm, and much more attention has been paid to the quantification of entanglement. Two measures of entanglement, formation and distillation [15,16] were also studied and recognized as "good" entanglement measures.In studying quantum entanglement, the density matrices are often used. It should be mentioned that density matrix can represent different physical quantities. In the case of proper mixture, the density matrix represents the averaged "state" of an ensemble of "molecules", while the improper mixture describes the averaged "state" of a subsystem in a coupled quantum system. Though the mathematical expressions are the same, their physical properties are quite differ-*Corresponding author (email: gllong@mail.tsinghua.edu.cn) ent [49,50]. In studying quantum entanglement, we are actually using the improper mixture meaning of the density matrix. The reduced density matrix is obtained by tracing out other degrees of freedom of a composite quantum system. Based on separating the correlations encoded by a density matrix into a common set of marginals, Partovi [37] proposed a measurement in which N!/2 quantities are used to quantify an N-qubit system. In the case of N 3, a "good" measurement [38] can be constructed from the arithmetic average entropy of single reduced density matrices. Realizing the lack of one-qubit reduction, Higuchi et al. [51,52] proposed using the arithmetic mean of two-particle entropies as a measure of entanglement, and reported on a four-qubit entangled state:which is more entangled than the four-qubit GHZ state.

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confidence: 99%

Entanglement of linear cluster states in terms of averaged entropies

Cao

Long

2013

Chin. Sci. Bull.

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“…quantum entanglement, quantum interference, common environment Citation: Man Z X, Su F, Xia Y J. Stationary entanglement of two atoms in a common reservoir. Chin Sci Bull, 2013Bull, , 58: 2423Bull, -2429Bull, , doi: 10.1007 Quantum entanglement is one of the most characteristic traits of quantum mechanics and has been recognized as an indispensable resource in realizing the quantum information technologies [1][2][3][4]. The fragility of entanglement, however, is one of the reasons that hampers its practical applications.…”

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confidence: 99%

“…Quantum entanglement is one of the most characteristic traits of quantum mechanics and has been recognized as an indispensable resource in realizing the quantum information technologies [1][2][3][4]. The fragility of entanglement, however, is one of the reasons that hampers its practical applications.…”

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confidence: 99%

Stationary entanglement of two atoms in a common reservoir

Man

Xia

2013

Chin. Sci. Bull.

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We study the dynamics of two entangled atoms interacting with a common structured reservoir. By means of the exact solution of atomic dynamics, we show a novel quantum interference controlled by the relative phase of initial entangled state of the atoms. The quantum interference has a great influence on trapped excited-state population and stationary entanglement of the atoms. In particular, we construct an explicit condition under which atomic stationary entanglement can grow over their initial value. quantum entanglement, quantum interference, common environment Citation: Man Z X, Su F, Xia Y J. Stationary entanglement of two atoms in a common reservoir. Chin Sci Bull, 2013Bull, , 58: 2423Bull, -2429Bull, , doi: 10.1007 Quantum entanglement is one of the most characteristic traits of quantum mechanics and has been recognized as an indispensable resource in realizing the quantum information technologies [1][2][3][4]. The fragility of entanglement, however, is one of the reasons that hampers its practical applications. The unavoidable coupling to the surrounding environment(s), whether intentionally or accidentally, is a serious obstacle since it always leads to the loss of open system's information [5]. Worse still, the entanglement may be terminated even in a finite time, a phenomenon called entanglement sudden death [6][7][8][9]. Therefore, the study on entanglement dynamics , namely, to know the residual amount of entanglement after a certain period of time evolution, is relevant to both the fundamental characters and applications of entanglement. In this connection, the issue of entanglement control becomes more and more important and a lot of methods [35][36][37][38][39][40] have been proposed to prolong the service time of entanglement or to preserve a long-lived stationary entanglement.The realization of decay mechanism proves to be effective in designing strategy to fight against the deterioration of entanglement. The dissipative interaction between individual quantum system with its environment is a usual mechanism *Corresponding author (email: manzhongxiao@163.com) spoiling the entanglement of a composite system. An emblematic example of the dissipative interaction is the spontaneous emission of a photon by a two-level atom (qubit) into a vacuum environment of electromagnetic-field modes. Therefore, the methods that can trap the excited-state population would be applicable for entanglement preservation. It has been shown [36] in environments, such as photonic band-gap materials, structured so as to inhibit spontaneous emission of individual atoms, the entanglement of two independent atoms can be trapped. Besides the special structure of the environment, [37] shows the vacuum-induced coherence [41] that can lead to quenching of spontaneous emission in atomic systems can also lead to preservation of atomic entanglement. For several qubits interacting with a same environment [23,24,26,27,35] and the total Hamiltonian is highly symmetric, there may exist a decoherence-free subspace and the stationar...

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“…Derivations of new and stronger Bell inequalities are one of the most important and challenging subjects in quantum information processing. Since Bell's work, there were many important generalizations such as [2][3][4][5][6][7][8][9][10][11] and references therein.…”

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confidence: 99%

Characterization of four-qubit states via Bell inequalities

2013

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A set of Bell inequalities classifying the quantum entanglement of four-qubit states is presented. These inequalities involve only two measurement settings per observer and can characterize fully separable, bi-separable and tri-separable quantum states. In addition, a quadratic inequality of the Bell operators for four-qubit systems is derived. Bell inequalities, separability, Bell operatorsCitation: Zhao H, Zhang X H, Fei S M, et al. Characterization of four-qubit states via Bell inequalities. Chin Sci Bull, 2013Bull, , 58: 2334Bull, -2339Bull, , doi: 10.1007 The Bell inequality [1] provided the first possibility to distinguish experimentally between quantum-mechanical predictions and those of local realistic models. Derivations of new and stronger Bell inequalities are one of the most important and challenging subjects in quantum information processing. Since Bell's work, there were many important generalizations such as [2-11] and references therein. The Bell inequalities presented in [12] involve only two measurement settings per observer and can detect perfectly the quantum entanglement of the generalized GHZ states. By using the idea in constructing Bell operators [12], a set of new Bell inequalities are given in [13], which gives rise to a finer classification of the entanglement for three-qubit systems.The entanglement of four-qubit systems has been treated in terms of Bell inequalities of Mermin-Klyshko type. In [14] the quantum nonlocality of some four-qubit states, the GHZ state, W state, cluster state and the state proposed in [15], has been investigated, towards the optimal violations of the Bell inequality for these states. The classification of entanglement has been also studied in such as [16][17][18][19] with linear inequalities for qubit systems and [20] with non-linear inequalities for detecting bi-separable states in arbitrary dimensional quantum systems.In this work, we study the quantum entanglement of four-*Corresponding author (email: zhaohui@bjut.edu.cn) qubit systems by using the idea in constructing Bell operators in [12]. We generalize the results of three-qubit systems in [13] to four-qubit systems. It has been shown that the standard Werner-Wolf-Żukowski-Brukner (WWZB) inequalities cannot detect the entanglement of the generalized Greenberger-Horne-Zeilinger (GHZ) states given by |ψ = cos α|0, ..., 0 + sin α|1, ..., 1 with 0 α π/4 [21, 22]. However, the Bell operators constructed in the way provided in [12] can detect the entanglement of the generalized GHZ state wholly. Our Bell operators are constructed by using the idea in [12]. The resulted Bell inequalities can distinguish fully separable, bi-separable and tri-separable states of a four-qubit system. Moreover, these linear Bell inequalities involve only two measurement settings per observer. Analytical formulas of the average values of the Bell operators for four-qubit systems are also derived. And a quadratic inequality of the Bell operators for all four-qubit systems has been presented. Explicit geometrical pictures show t...

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An entanglement criterion for states in infinite-dimensional multipartite quantum systems

Cited by 11 publications

References 20 publications

Entanglement of linear cluster states in terms of averaged entropies

Entanglement of linear cluster states in terms of averaged entropies

Stationary entanglement of two atoms in a common reservoir

Characterization of four-qubit states via Bell inequalities

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