Precise detection of multipartite entanglement in four-qubit Greenberger–Horne–Zeilinger diagonal states

Abstract

We propose a method of constructing the separability criteria for multipartite quantum states on the basis of entanglement witnesses. The entanglement witnesses are obtained by finding the maximal expectation values of Hermitian operators and then optimizing over all possible Hermitian operators. We derive a set of tripartite separability criteria for the four-qubit Greenberger-Horne-Zeilinger (GHZ) diagonal states. The derived criterion set contains four criteria that are necessary and sufficient for the tripartite separability of the highly symmetric four-qubit GHZ diagonal states; the criteria completely account for the numerically obtained boundaries of the tripartite separable state set. One of the criteria is just the tripartite separability criterion of the four-qubit generalized Werner states.PACS number(s): 03.65.Ud; 03.67.Mn;

Robustness of Entanglement for W and Greenberger-Horne-Zeilinger Mixed States

“…For entanglement quantification [17], there are entanglement entropy [18,19], the relative entropy of entanglement [20,21] and robustness of entanglement [2,5,6]. Building upon these foundations, as significant quantum states widely used [22,23] in the field of quantum information, the robustness of entanglement for both pure W states and pure Greenberger-Horne-Zeilinger(GHZ) states has been comprehensively studied [24][25][26]. However, a pure state will become a mixed state in the decoherence environment.…”

Entanglement Detection: A Scoping Review

“…Entanglement detection, which is the process of determining whether a particular state is entangled or not, has proven to be difficult, especially in high-dimensional systems [12,13]. Entanglement detection is required to fully understand the structure of a state system, making it a hot topic in quantum technology [14].…”

Entanglement witnesses of four-qubit tripartite separable quantum states*

“…Quantum Fisher information (QFI) [8][9][10] has been used in the detection of the entanglement and the k-nonseparability of multipartite quantum systems. Entanglement witness [11] is also widely used and appropriate for multipartite systems in entanglement detection [12][13][14][15][16][17]. Theoretically, an entanglement witness exists which can be a sufficient and necessary condition for detecting entanglement.…”