We construct a set of criteria detecting genuine multipartite entanglement in arbitrary dimensional multipartite systems. These criteria are optimally suited for detecting multipartite entanglement in $n$ -qubit Dicke states with $m$ excitations, as shown in exemplary cases. Furthermore, they can be employed to detect multipartite entanglement in different states related to quantum cloning, decoherence-free communication, and quantum secret sharing. In a detailed analysis, we show that the criteria are also more robust to noise than any other criterion known so far, especially with increasing system size. Furthermore, it is shown that the number of required local observables scales only polynomially with size, thus making the criteria experimentally feasible.We construct a set of criteria detecting genuine multipartite entanglement in arbitrary dimensional multipartite systems. These criteria are optimally suited for detecting multipartite entanglement in $n$-qubit Dicke states with $m$ excitations, as shown in exemplary cases. Furthermore, they can be employed to detect multipartite entanglement in different states related to quantum cloning, decoherence-free communication, and quantum secret sharing. In a detailed analysis, we show that the criteria are also more robust to noise than any other criterion known so far, especially with increasing system size. Furthermore, it is shown that the number of required local observables scales only polynomially with size, thus making the criteria experimentally feasible.

arXiv:1011.4579Physical Review AApr 18, 201156 citations

An algebraic approach to the study of multipartite entanglement

Sara Di Martino, Benedetto Militello, ANTONINO MESSINA

arXiv:1204.2227Journal of Russian Laser ResearchJan 1, 20131 citation

Several families of entanglement criteria for multipartite quantum systems based on generalized Wigner-Yanase skew information and variance

Yan Hong, Hao, Xinlan, Limin Gao

Quantum entanglement plays a critical role in many quantum applications, but detecting entanglement, especially in multipartite or high-dimensional quantum systems, remains a challenge. In this paper, we propose several families of entanglement criteria for detecting entanglement in multipartite or high-dimensional quantum states by the generalized Wigner-Yanase skew information $I^s(ρ,X)$ for $-1\leq s\leq0$ and variance. We also reveal a complementary character between the criteria based on the generalized Wigner-Yanase skew information and an alternative one based on variance through specific examples. We illustrate the merits of these criteria and show that the combination of the entanglement criteria has a stronger detection capability, as it is capable of detecting entangled states that remain unrecognized by other criteria.Quantum entanglement plays a critical role in many quantum applications, but detecting entanglement, especially in multipartite or high-dimensional quantum systems, remains a challenge. In this paper, we propose several families of entanglement criteria for detecting entanglement in multipartite or high-dimensional quantum states by the generalized Wigner-Yanase skew information $I^s(ρ,X)$ for $-1\leq s\leq0$ and variance. We also reveal a complementary character between the criteria based on the generalized Wigner-Yanase skew information and an alternative one based on variance through specific examples. We illustrate the merits of these criteria and show that the combination of the entanglement criteria has a stronger detection capability, as it is capable of detecting entangled states that remain unrecognized by other criteria.

arXiv:2409.11273Sep 17, 20240 citations

n

-qubit Dicke states with

m

excitations, as shown in exemplary cases. Furthermore, they can be employed to detect multipartite entanglement in different states related to quantum cloning, decoherence-free communication, and quantum secret sharing. In a detailed analysis, we show that the criteria are also more robust to noise than any other criterion known so far, especially with increasing system size. Furthermore, it is shown that the number of required local observables scales only polynomially with size, thus making the criteria experimentally feasible.

I^s(ρ,X)

for

-1\leq s\leq0

and variance. We also reveal a complementary character between the criteria based on the generalized Wigner-Yanase skew information and an alternative one based on variance through specific examples. We illustrate the merits of these criteria and show that the combination of the entanglement criteria has a stronger detection capability, as it is capable of detecting entangled states that remain unrecognized by other criteria.