Erratum to “Measures and dynamics of entangled states” [Phys. Rep. 415 (2005) 207–259]

Mintert, Florian; Carvalho, André; Kuś, Marek; Buchleitner, Andreas

doi:10.1016/j.physrep.2005.08.001

Cited by 131 publications

(244 citation statements)

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“…Quite generally, the decay of entanglement is non-exponential, and it may lead to separability at finite times, before each part reaches its final state [22][23][24][25][26][27][28][29][30][31][32][33]. The finitetime disappearance of entanglement, sometimes called "sudden-death of entanglement" [28,33] was experimentally demonstrated by Almeida et al [32].…”

Section: Introductionmentioning

confidence: 99%

Quantum correlations as precursors of entanglement

Auyuanet

2010

Phys. Rev. A

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We show that for two initially excited qubits, interacting via dipole forces and with a common reservoir, entanglement is preceded by the emergence of quantum and classical correlations. After a time lag, entanglement finally starts building up, giving rise to a peculiar entangled state, with very small classical correlations. Different measures of quantum correlations are discussed, and their dynamics are compared and shown to lead to coincident values of these quantifiers for several ranges of time.

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Section: Introductionmentioning

confidence: 99%

Quantum correlations as precursors of entanglement

Auyuanet

2010

Phys. Rev. A

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“…which, however, is not suitable, since the decomposition (3) is not unique: M would thus give rise to different values of entanglement for different valid decompositions of ρ [9], inconsistently with the general requirements for a bona fide entanglement measure [5,6]. The proper definition of M (ρ) therefore is the infimum of all possible averages M [10], but holds two main drawbacks: (i) it turns into a hard numerical problem for higher dimensional or multipartite systems, and, (ii) even for bipartite qubits, where analytical solutions for some measures M (ρ) are known [8], there is no obvious interpretation of this optimal decomposition, in physical terms.…”

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confidence: 99%

“…Under realistic laboratory conditions, however, entanglement is degraded through uncontrolled coupling to the environment. It is of crucial practical importance to quantify this degradation process [1][2][3], though also extremely difficult in general, due to the intricate mathematical notions upon which our understanding of entanglement relies [4][5][6]. Up to now, no general observable is known which would complement such essentially formal concepts with a specific experimental measurement setup.…”

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confidence: 99%

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Optimal Dynamical Characterization of Entanglement

et al. 2007

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We show that the time evolution of entanglement under incoherent environment coupling can be faithfully recovered by monitoring the system according to a suitable measurement scheme.PACS numbers: 03.67.Mn,03.65.Yz,42.50.Lc Quantum information processing requires the ability to produce entangled states and coherently perform operations on them. Under realistic laboratory conditions, however, entanglement is degraded through uncontrolled coupling to the environment. It is of crucial practical importance to quantify this degradation process [1][2][3], though also extremely difficult in general, due to the intricate mathematical notions upon which our understanding of entanglement relies [4][5][6]. Up to now, no general observable is known which would complement such essentially formal concepts with a specific experimental measurement setup.In the present Letter, we come up with a dynamical characterization of entanglement, through the continuous observation of a quantum system which evolves under incoherent coupling to an environment. We show that, at least for small, yet experimentally relevant systems, there is an optimal measurement strategy to monitor the entanglement of the time evolved, mixed system state. Mixed state entanglement is then given as the average entanglement of the pure states generated by single realisations of the optimal measurement-induced, stochastic time evolution.Consider a bipartite quantum system composed of subsystems A and B, interacting with its environment. Due to this coupling, an initially pure state |Ψ 0 of the composite system will evolve into a mixed state ρ(t), in a way governed by the master equatioṅwhere the Hamiltonian H generates the unitary system dynamics. The superoperators L k describe the effects of the environment on the system, and, for a Markovian bath, have the standard form [7]where the operators J k depend on the specific physical situation under study.To extract the time evolution of entanglement under this incoherent dynamics, one solution is to evaluate a given entanglement measure M (ρ) for the solution ρ(t), at all times t. One starts from one of the known pure state measures M (Ψ) [5,6,8], together with a pure state decomposition of ρ,where the p i are the positive, normalized weights of each pure state |Ψ i . The most naive generalization for a mixed state would then be to consider the averagewhich, however, is not suitable, since the decomposition (3) is not unique: M would thus give rise to different values of entanglement for different valid decompositions of ρ [9], inconsistently with the general requirements for a bona fide entanglement measure [5,6]. The proper definition of M (ρ) therefore is the infimum of all possible averages M [10], but holds two main drawbacks: (i) it turns into a hard numerical problem for higher dimensional or multipartite systems, and, (ii) even for bipartite qubits, where analytical solutions for some measures M (ρ) are known [8], there is no obvious interpretation of this optimal decomposition, in physical terms. Our a...

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“…the concurrence c(̺) [20,21] provides a measure of entanglement. In general, the calculation of c(̺) is a formidable task.…”

Section: Decoherence Models and General Propertiesmentioning

confidence: 99%

Decoherence-based exploration ofd-dimensional one-way quantum computation: Information transfer and basic gates

Tame¹,

Paternostro²,

Hadley

et al. 2006

Phys. Rev. A

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We study the effects of amplitude and phase damping decoherence in d-dimensional one-way quantum computation (QC). Our investigation shows how information transfer and entangling gate simulations are affected for d ≥ 2. To understand motivations for extending the one-way model to higher dimensions, we describe how d-dimensional qudit cluster states deteriorate under environmental noise. In order to protect quantum information from the environment we consider the encoding of logical qubits into physical qudits and compare entangled pairs of linear qubit-cluster states with single qudit clusters of equal length and total dimension. Our study shows a significant reduction in the performance of one-way QC for d > 2 in the presence of Markovian type decoherence models.

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Erratum to “Measures and dynamics of entangled states” [Phys. Rep. 415 (2005) 207–259]

Cited by 131 publications

References 0 publications

Quantum correlations as precursors of entanglement

Quantum correlations as precursors of entanglement

Optimal Dynamical Characterization of Entanglement

Decoherence-based exploration ofd-dimensional one-way quantum computation: Information transfer and basic gates

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