Triangle Measure of Tripartite Entanglement

Xie, Songbo; Eberly, J. H.

doi:10.1103/physrevlett.127.040403

Cited by 79 publications

(77 citation statements)

References 42 publications

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“…It is important to note that the X states density matrix is physically realizable in various scenarios [45,46]. For instance, pseudo-pure states in NMR spin systems are essentially of the same form as (17). More specifically, a highly mixed thermal state of the form can be described through a traceless deviation of maximally mixed state, i.e., ρ t (1 − ∑ i σ i z )/n, which upon an action of completely positive and trace preserving map yields a density matrix ρ P = T(ρ t ) = 1/n − α(ρ pp − 1/n), with ρ pp representing a pure state, representing a small deviation parameter, and α, a factor determining signal loss, is essentially of the same form as the Werner state density matrix, with the mixing parameter x = α [47].…”

Section: Ghz-class Werner Statesmentioning

confidence: 99%

“…Furthermore, protocols involving parties at several different spatially separated locations necessarily require multipartite correlation. Therefore, the characterization and quantification of genuine multipartite correlation has received significant interest [12][13][14][15][16][17]. Entanglement in bipartite two-qubit systems is well understood through several measures such as concurrence [18], entanglement of formation [19], negativity [20], etc.…”

Section: Introductionmentioning

confidence: 99%

“…For the faithful quantification of three-party correlations, which are used as a resource in teleportation and other quantum tasks, one requires a genuine correlation quantifier, which is zero for all biseparable and product states and non-zero for all non-biseparable states [14]. There exists several measures of genuine entanglement for pure tripartite systems [17,21,22]; however, quantifying genuine entanglement for a general three-qubit system still remains a challenging task. The author of [15] has defined a measure "genuine multipartite concurrence", a quantifier of genuine multipartite entanglement, which is reduced to the Wooter's bipartite concurrence for two qubits.…”

Section: Introductionmentioning

confidence: 99%

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Exact Time Evolution of Genuine Multipartite Correlations for N-Qubit Systems in a Common Thermal Reservoir

et al. 2022

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We investigate the dynamical evolution of genuine multipartite correlations for N-qubits in a common reservoir considering a non-dissipative qubits-reservoir model. We derive an exact expression for the time-evolved density matrix by modeling the reservoir as a set of infinite harmonic oscillators with a bilinear form of interaction Hamiltonian. Interestingly, we find that the choice of two-level systems corresponding to an initially correlated multipartite state plays a significant role in potential robustness against environmental decoherence. In particular, the generalized W-class Werner state shows robustness against the decoherence for an equivalent set of qubits, whereas a certain generalized GHZ-class Werner state shows robustness for inequivalent sets of qubits. It is shown that the genuine multipartite concurrence (GMC), a measure of multipartite entanglement of an initially correlated multipartite state, experiences an irreversible decay of correlations in the presence of a thermal reservoir. For the GHZ-class Werner state, the region of mixing parameters for which there exists GMC, shrinks with time and with increase in the temperature of the thermal reservoir. Furthermore, we study the dynamical evolution of the relative entropy of coherence and von-Neumann entropy for the W-class Werner state.

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Section: Ghz-class Werner Statesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Exact Time Evolution of Genuine Multipartite Correlations for N-Qubit Systems in a Common Thermal Reservoir

et al. 2022

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“…A stronger version of this requirement is that entanglement cannot increase on average under stochastic LOCC (SLOCC). For two-qubit entangled states, there exists only a single SLOCC equivalent class, and all the entanglement monotones agree on which state is more entangled [8,9]. However, the complexity of multipartite entanglement grows dramatically with the increasing number of parties.…”

mentioning

confidence: 99%

“…Substantial achievements have been made in the research of multipartite entanglement measures [30][31][32][33][34][35], but most of these measures do not fully satisfy Definition 1 [9]. Worst of all, very few GME measures are available.…”

mentioning

confidence: 99%

Geometric mean of bipartite concurrences as a genuine multipartite entanglement measure

Li,

Shang

2021

Preprint

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In this work we propose the geometric mean of bipartite concurrences as a genuine multipartite entanglement measure. This measure achieves the maximum value for absolutely maximally entangled states and has desirable properties for quantifying potential quantum resources. The simplicity and symmetry in the definition facilitates its computation for various multipartite entangled states including the GHZ states and the W states. With explicit examples we show that our measure results in distinct entanglement orderings from other measures, and can detect differences in certain types of genuine multipartite entanglement while other measures cannot. These results justify the practical application of our measure for tasks involving genuine multipartite entanglement.

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A Genuine Multipartite Entanglement Measure Generated by the Parametrized Entanglement Measure

Shi,

Chen

2023

Annalen der Physik

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A genuine multipartite entanglement measure based on the geometric method is investigated in this paper. This measure has desirable properties for quantifying the genuine multipartite entanglement. A lower bound of the genuine multipartite entanglement measure derived with the fidelity‐based method is then presented. The advantages of the measure proposed here with other measures are also presented. At last, examples are presented to show that the genuine entanglement measure has distinct entanglement ordering from other measures.

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Triangle Measure of Tripartite Entanglement

Cited by 79 publications

References 42 publications

Exact Time Evolution of Genuine Multipartite Correlations for N-Qubit Systems in a Common Thermal Reservoir

Exact Time Evolution of Genuine Multipartite Correlations for N-Qubit Systems in a Common Thermal Reservoir

Geometric mean of bipartite concurrences as a genuine multipartite entanglement measure

A Genuine Multipartite Entanglement Measure Generated by the Parametrized Entanglement Measure

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