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arXiv:2206.02232 · Annalen der Physik

A Genuine Multipartite Entanglement Measure Generated by the Parametrized Entanglement Measure

Xian Shi, Lin Chen

Published Oct 29, 2023• 12 citations
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Abstract

Abstract 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.

DOI
10.1002/andp.202300305

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Abstract 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.
In this paper, 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 WWW 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 potential application of our measure for tasks involving genuine multipartite entanglement.
ABSTRACT Entanglement is a fundamental resource in quantum information science. In this work, we introduce the geometric total concurrence (GTC), a new measure of genuine multipartite entanglement (GME) for ‐partite systems based on the concept of total concurrence. The GTC satisfies a key criterion by assigning higher entanglement to GHZ states than to W states. We derive analytically computable lower bounds for the GTC using PPT and realignment criteria. Furthermore, we show that the GTC induces an entanglement ordering distinct from existing measures, providing a unique perspective on multipartite correlations. Through detailed examples, we demonstrate that the GTC offers improved sensitivity in detecting entanglement and sharper discrimination among different types of entangled states, establishing it as a practical tool for characterizing and quantifying GME.
Experimentally quantifying entanglement and coherence are extremely important for quantum resource theory. However, because the quantum state tomography requires exponentially growing measurements with the number of qubits, it is hard to quantify entanglement and coherence based on the full information of the experimentally realized multipartite states. Fortunately, other methods have been found to directly measure the fidelity of experimental states without quantum state tomography. Here we present a fidelity-based method to derive experimentally accessible lower bounds for measures of genuine multipartite entanglement and coherence. On the one hand, the method works for genuine multipartite entanglement measures including the convex-roof extended negativity, the concurrence, the G-concurrence, and the geometric measure for genuine multipartite entanglement. On the other hand, the method also delivers observable lower bounds for the convex roof of the l1l_{1}l1​-norm of coherence, the geometric measure of coherence, and the coherence of formation. Furthermore, all the lower bounds are based on the fidelity between the chosen pure state and the target state, and we obtain the lower bounds of several real experimental states as examples of our results.
Abstract Quantifying genuine entanglement is a crucial task in quantum information theory. In this work, a new genuine multipartite entanglement measure based on informationally complete entanglement is proposed, termed the informationally complete genuine multipartite entanglement measure(ICGMEM). A set of entanglement inequalities for pure states in ‐partite systems is first established based on constraints on entanglement distribution. These inequalities reveal that the pairwise entanglement between any individual part of the system cannot exceed the collective entanglement of the remaining parts. Building on these inequalities, a series of geometric structures called informationally complete entanglement measure triangles is constructed and the ICGMEM is defined based on the geometric mean area of these triangles. These results demonstrate that the ICGMEM provides a more refined characterization of entanglement compared to existing well‐known measures. Furthermore, it is shown that the ICGMEM significantly enhances computational efficiency for analyzing genuinely entangled pure states, achieving up to a twofold improvement when the number of subsystems is sufficiently large. Through detailed examples, the advantages of the ICGMEM are illustrated, highlighting its effectiveness in distinguishing and quantifying entanglement in multipartite systems. This work can better advance the theoretical understanding of genuine multipartite entanglement.
ABSTRACT Characterizing the entanglement in multipartite quantum systems remains a central challenge in the theory of quantum entanglement. We establish a comprehensive framework for constructing ‐entanglement measures by leveraging bipartite entanglement measures and general ‐entanglement measures () with arithmetic and geometric averaging schemes. Numerical examples demonstrate that these measures outperform the existing ones, such as ‐ME concurrence, geometric mean (k‐GM) concurrence, and the generalized ‐entanglement measure by inducing distinct entanglement orderings and offering superior resolution. Furthermore, we reveal the operational relationship between the ‐entanglement and the local quantum coherence, verifying that the persistence of entanglement is intrinsically constrained by the system's capacity to maintain the local coherence. Finally, to overcome the inherent limitation of the conventional three‐tangle in characterizing the genuine multipartite entanglement of the GHZ‐W mixed states, we design a novel GME measure. Numerical results confirm that this measure effectively eliminates the detection blind spots where vanishes, providing a complete and practical mathematical tool for the quantitative analysis of genuine multipartite quantum correlations.
Genuine Multipartite Entanglement Measure Based on ααα-concurrence
Quantifying genuine entanglement is a crucial task in quantum information theory. Based on the geometric mean of bipartite ααα-concurrences among all bipartitions, we present a class of well-defined genuine multipartite entanglement (GME) measures GαααC with one parameter ααα for arbitrary multipartite states. We show that the GαααC is of continuity for any multipartite pure states. By utilizing the related symmetry, analytical results of GαααC are derived for any nnn-qubit GHZ states and W states, which show that the GHZ states are more genuinely entangled than the W states. With explicit examples, we demonstrate that the GαααC can distinguish different GME states that other GME measures fail to. These results justify the potential applications of GαααC in characterizing genuine multipartite entanglements.