Postulates for measures of genuine multipartite correlations

Bennett, Charles H.; Grudka, Andrzej; Horodecki, Michał; Horodecki, Paweł; Horodecki, Ryszard

doi:10.1103/physreva.83.012312

Cited by 83 publications

(119 citation statements)

References 23 publications

(35 reference statements)

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“…Genuine correlations represent the amount of correlations that cannot be accounted for considering any of the possible reduced subsystems: An n-partite state has genuine n-partite correlations if it is non-product in every bipartite cut (this definition is in agreement with the general criteria given in Ref. [11]). According to this criterion, genuine total correlations T (n) ( ) coincide with the distance, measured through the relative entropy, between and the closest state with no n-partite correlations, that is, the closest state which is product at least along a bipartite cut [13].…”

Section: Genuine Multipartite Correlationssupporting

confidence: 64%

“…As in the case of entanglement [3], the extension to the multipartite scenario is not trivial. A series of postulates any good measure of multipartite correlations should obey was given by Bennett et al [11]. Three main generalizations of quantum discord to the multipartite case have been proposed: Rulli and Sarandy introduced the so-called global discord (GD) which is a natural extension of a symmetrized version of the QD and is based on a collective measurement [12], Modi and co-workers proposed a unified view of correlations that applies in both the bipartite and the multipartite scenarios based on the use of the relative entropy to quantify the 'distance' between states [13], and in Ref.…”

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confidence: 99%

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Multipartite quantum and classical correlations in symmetric n-qubit mixed states

Giorgi

Campbell

2016

Quantum Inf Process

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We discuss how to calculate genuine multipartite quantum and classical correlations in symmetric, spatially invariant, mixed n-qubit density matrices. We show that the existence of symmetries greatly reduces the amount of free parameters to be optimized in order to find the optimal measurement that minimizes the conditional entropy in the discord calculation. We apply this approach to the states exhibited dynamically during a thermodynamic protocol to extract maximum work. We also apply the symmetry criterion to a wide class of physically relevant cases of spatially homogeneous noise over multipartite entangled states. Exploiting symmetries we are able to calculate the non-local and genuine quantum features of these states and note some interesting properties.

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Section: Genuine Multipartite Correlationssupporting

confidence: 64%

mentioning

confidence: 99%

Multipartite quantum and classical correlations in symmetric n-qubit mixed states

Giorgi

Campbell

2016

Quantum Inf Process

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“…One might expect that genuinely n-partite entanglement gives rise to non-vanishing correlations between all n subsystems. This is incorrect, at least when correlations are quantified as average values of a product of local measurement results [3,4] (for a discussion on quantum correlations without classical correlations, see e.g. [5]).…”

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confidence: 99%

Detecting genuine multipartite entanglement of pure states with bipartite correlations

et al. 2013

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Monogamy of bipartite correlations leads, for arbitrary pure multi-qubit states, to simple conditions able to indicate various types of multipartite entanglement by being capable to exclude the possibility of k-separability.PACS numbers: 03.67.MnFor bipartite systems the phenomenon of quantum entanglement [1, 2] manifests itself in correlations. One might expect that genuinely n-partite entanglement gives rise to non-vanishing correlations between all n subsystems. This is incorrect, at least when correlations are quantified as average values of a product of local measurement results [3,4] (for a discussion on quantum correlations without classical correlations, see e.g. [5]). Thus, in order to detect genuine multipartite entanglement of certain states one has to rely on correlations between smaller number of subsystems [6].Here we discuss global features of multiparty qubit pure states, which can be deduced from their bipartite correlations. We shall use the property of monogamy of correlations [7]. Another approach has recently been put forward by Würflinger et al. [8] who have shown that some non-entangled reduced density operators can be linked with global entangled states.Monogamy of quantum correlations can be used for entanglement detection [9]. We will use it to derive a criterion for genuine multipartite entanglement. Monogamy was also employed in studies of quantum marginal problem, i.e. conditions for existence of a global quantum state given its marginals [10], security of quantum key distribution [11], and to show that correlations between macroscopic measurements ought to be classical [12]. It leads to efficient methods of solving strongly correlated multipartite quantum lattice systems [13].States of n qubits (two-level quantum systems) have density matrices of the following form:

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“…However the crucial obstacle for further development is the absence of the unified understanding of the multipartite entanglement [18,19]. Whereas the maximally entangled state can be defined unambiguously for bipartite systems, what is the maximally entangled state for multipartite systems is unclear until now [19]. Fortunately it is well accepted that the fully separable state can be defined as…”

Section: Introductionmentioning

confidence: 99%

“…The connection of multipartite entanglement and quantum phase transition has been discussed in some special models [14][15][16][17]. However the crucial obstacle for further development is the absence of the unified understanding of the multipartite entanglement [18,19]. Whereas the maximally entangled state can be defined unambiguously for bipartite systems, what is the maximally entangled state for multipartite systems is unclear until now [19].…”

Section: Introductionmentioning

confidence: 99%

Overlap of quantum many-body states with a separable state and phase transitions in the Dicke model: Zero and finite temperature

Cui

2010

Phys. Rev. A

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Overlap with the separable state is introduced in this paper for the purpose of characterizing the overall correlation in many-body systems. This definition has clear geometric and physical meaning, and moreover can be considered as the generalization of the concept-Anderson Orthogonality Catastrophe. As an exemplification, it is used to mark the phase transition in the Dicke model for zero and finite temperature. And our discussion shows that it can faithfully reflect the phase transition properties of this model whether for zero or finite temperature. Furthermore the overlap for ground state also indicates the appearance of multipartite entanglement in Dicke model.

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Postulates for measures of genuine multipartite correlations

Cited by 83 publications

References 23 publications

Multipartite quantum and classical correlations in symmetric n-qubit mixed states

Multipartite quantum and classical correlations in symmetric n-qubit mixed states

Detecting genuine multipartite entanglement of pure states with bipartite correlations

Overlap of quantum many-body states with a separable state and phase transitions in the Dicke model: Zero and finite temperature

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