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Laser Physics Letters

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

Yan Hong, Xinlan Hao, Limin Gao

Published Nov 6, 2024• 1 citation
Publisher

Abstract

Abstract 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 ⩽ s ⩽ 0 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.

DOI
10.1088/1612-202x/ad8cc6

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Abstract 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 ⩽ s ⩽ 0 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 Is(ρ,X)I^s(ρ,X)Is(ρ,X) for −1≤s≤0-1\leq s\leq0−1≤s≤0 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.
Abstract Multipartite quantum entanglement, as a core quantum resource, is fundamental to the advancement of quantum science and technology. In multipartite quantum systems, there are two kinds of quantum entanglement: k -nonseparability and k -partite entanglement. In this paper, we propose sufficient criteria for detecting k -nonseparability and k -partite entanglement by using the generalized Wigner–Yanase skew information and mutually unbiased measurements. Examples are given to demonstrate the detection capability and advantages of these criteria. As an application, an example of recognizing the networks by detecting the depth of quantum networks is given.
The detection of multipartite entanglement in multipartite quantum systems is a fundamental and key issue in quantum information theory.In this paper, we investigate kkk-nonseparability and kkk-partite entanglement of NNN-partitequantum systems from the perspective of the generalized Wigner-Yanase skew information introduced by Yang etetet alalal.[\href{https://doi.org/10.1103/PhysRevA.106.052401}{Phys. Rev. A \textbf{106}, 052401 (2022)}]. More specifically, we develop two different approaches in form of inequalities to construct entanglement criteria, which are expressed in terms of the generalized Wigner-Yanase skew information.Any violation of these inequalities by a quantum state reveals its kkk-nonseparability or kkk-partite entanglement,so these inequalities present the hierarchic classifications of kkk-nonseparability or kkk-partite entanglement for all NNN-partite quantum states from NNN-nonseparability to 222-nonseparability or from 222-partite entanglement to NNN-partite entanglement, which are more refined than well-known ways. It is shown that our results reveal some kkk-nonseparability and kkk-partite entanglement that remain undetected by other methods,and these are illustrated through some examples.
Abstract We propose an entanglement criterion, specially designed for mixed states, based on uncertainty relation and the Wigner–Yanase skew information. The variances in this uncertainty relation do not involve any classical mixing uncertainty, and is therefore purely of quantum mechanical nature. We show that a large class of mixed entangled states can be characterized by our criterion. We demonstrate its utility for several generalized mixed entangled state including two-qubit and two-qutrit Werner states and it turns out, for the states discussed in this paper, to be stronger than any other known criterion in identifying the correct domain of relevant parameters for entanglement. The relevant uncertainty relation reduces to the Schrodinger–Robertson inequality for pure states.
We propose an entanglement criterion, specially designed for mixed states, based on uncertainty relation and the Wigner-Yanase skew information. The variances in this uncertainty relation does not involve any classical mixing uncertainty, and thus turns out to be purely of quantum mechanical nature. We show that any mixed entangled state can be characterized by our criterion. We demonstrate its utility for several generalized mixed entangled state including Werner states and it turns out to be stronger than any other known criterion in identifying the correct domain of relevant parameters for entanglement. The proposed criterion reduces to the Schrodinger-Robertson inequality for pure states.
Multipartite entanglement plays an essential role in both quantum information science and many-body physics. Because of the exponentially large dimension and complex geometric structure of the state space, the detection of entanglement in many-body systems is extremely challenging in reality. Conventional means, like entanglement witness and entropy criterion, either highly depend on the prior knowledge of the studied systems or the detection capability is relatively weak. In this Letter, we propose a framework for designing multipartite entanglement criteria based on permutation moments, which have an effective implementation with either the generalized control-swap quantum circuits or the random unitary techniques. As an example, in the bipartite scenario, we develop an entanglement criterion that can detect bound entanglement and show strong detection capability in the multiqubit Ising model with a long-range XY Hamiltonian. In the multipartite case, the permutation-moment-based criteria can detect entangled states that are not detectable by any criteria extended from the bipartite case. Our framework also shows potential in entanglement quantification and entanglement structure detection.