Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Modern Physics Letters A

Separability criteria via states of projective two-designs

Alexey E. Rastegin

Published Jan 22, 2026• 0 citations
Publisher

Abstract

Special types of measurements are widely used in quantum information processing. The task to detect entangled states can arise within an intermediate stage of the protocol to be performed. It is inevitable in many questions, and it is desirable to study separability criteria derived with different choices of selected states. This study aims to examine such criteria for quantum measurements assigned to projective two-designs. The considered approaches use the so-called correlation measure and the corresponding correlation matrix. Separability criteria for multipartite systems are also derived.

DOI
10.1142/s0217732326500331

Related papers

Efficient k-separability criteria for mixed multipartite quantum states

Ting Gao, Yan Hong, Yao Lu +1 more

We investigate classification and detection of entanglement of multipartite quantum states in a very general setting, and obtain efficient $k$-separability criteria for mixed multipartite states in arbitrary dimensional quantum systems. These criteria can be used to distinguish $n-1$ different classes of multipartite inseparable states and can detect many important multipartite entangled states such as GHZ states, W states, anti W states, and mixtures thereof. They detect $k$-nonseparable $n$-partite quantum states which have previously not been identified. Here $k=2,3,\cdots,n$. No optimization or eigenvalue evaluation is needed, and our criteria can be evaluated by simple computations involving components of the density matrix. Most importantly, they can be implemented in today's experiments by using at most $\mathcal{O}(n^2)$ local measurements.

arXiv:1204.2864•Europhysics Letters (EPL)•Oct 1, 2013•49 citations

Enhancing some separability criteria in many-body quantum systems

Liang Bao Tang, Fan Wu

Abstract Quantum measurements based on mutually unbiased bases, mutually unbiased measurements and general symmetric informationally complete positive operator valued measurements, which are commonly used in quantum information and quantum computation. In this paper, by a broad class of informationally complete symmetric measurements and correlation matrices, some separability criteria are proposed for different quantum systems that are more robust and comprehensive than the corresponding criteria previously introduced L M Lai, T Li, S M Fei, and Z X Wang, (2018 Quantum Inf. Process., 17, 314); J W Shang, A Asadian, and H J Zhu, (2018 Phys. Rev. A 98, 022309). Furthermore, we extend the separability criteria of tripartite quantum systems to many-body systems. The proposed entanglement criteria may further enrich the relationship between quantum entanglement and measurement.

Physica Scripta•Apr 28, 2023•9 citations

Separability criteria and method of measurement for entanglement

Siti Munirah Mohd, Bahari Idrus, Muriati Bt. Mukhtar

Quantum computers have the potentials to solve certain problems faster than classical computers. In quantum computer, entanglement is one of the elements beside superposition. Recently, with the advent of quantum information theory, entanglement has become an important resource for Quantum Information and Computation. The purpose of this paper is to discuss the separability criteria and method of measurement for entanglement. This paper is aimed at viewing the method that has been proposed in previous works in bipartite and multipartite entanglement. The outcome of this paper is to classify the different method that used to measure entanglement for bipartite and multipartite cases including the advantage and disadvantage of each method.

AIP conference proceedings•Jan 1, 2014•1 citation

Separability and classification of multipartite quantum states

Pan-Wen Ma, Hui Zhao, Naihuan Jing

Abstract We study separability in arbitrary multipartite quantum systems based on principal base matrices. Necessary conditions are presented for different kinds of separable states. These conditions can give a complete classification of multipartite quantum states. While the usual Bloch representation of a density matrix uses three types of generators, the representation with principal base matrices has one uniform type of generator which simplifies computation. In this paper, we take advantage of this simplicity to derive useful and operational criteria to detect multipartite separability. We first obtain criteria on detecting 1 − 3 separable, 2 − 2 separable, 1 − 1 − 2 separable and fully separable four-partite quantum states. We then study k-separability for multipartite quantum states in arbitrary dimensions. Detailed examples are given to show that our criteria are able to detect more entanglement states than some existing criteria.

Laser Physics Letters•Nov 8, 2023•1 citation

Quantum Separability Criteria Based on Symmetric Measurements

Yu Lu, Wen Zhou, Meng Su +3 more

We propose experimentally feasible separability criteria for bipartite systems based on local symmetric measurements. Through detailed examples, we demonstrate that our criteria can detect entanglement more effectively compared to existing counterparts. Furthermore,we demonstrate the potential for our results to be generalized to general multipartite systems.

quant-pharXiv:2512.10380•Physical Review A•Dec 12, 2025•0 citations

Enhanced separability criteria based on symmetric measurements

Yu Lu, Hao-Fan Wang, Meng Su +2 more

We present separability criteria based on local symmetric measurements. These experimental plausible criteria are shown to be more efficient in detecting entanglement than the current counterparts by detailed examples. Furthermore, we generalize the separability criteria from bipartite to arbitrary multipartite systems. These criteria establish a richer connection between the quantum entanglement and the probabilities of local measurement outcomes.

quant-pharXiv:2512.22514•Advanced Quantum Technologies•Dec 30, 2025•0 citations
Special types of measurements are widely used in quantum information processing. The task to detect entangled states can arise within an intermediate stage of the protocol to be performed. It is inevitable in many questions, and it is desirable to study separability criteria derived with different choices of selected states. This study aims to examine such criteria for quantum measurements assigned to projective two-designs. The considered approaches use the so-called correlation measure and the corresponding correlation matrix. Separability criteria for multipartite systems are also derived.
We investigate classification and detection of entanglement of multipartite quantum states in a very general setting, and obtain efficient kkk-separability criteria for mixed multipartite states in arbitrary dimensional quantum systems. These criteria can be used to distinguish n−1n-1n−1 different classes of multipartite inseparable states and can detect many important multipartite entangled states such as GHZ states, W states, anti W states, and mixtures thereof. They detect kkk-nonseparable nnn-partite quantum states which have previously not been identified. Here k=2,3,⋯ ,nk=2,3,\cdots,nk=2,3,⋯,n. No optimization or eigenvalue evaluation is needed, and our criteria can be evaluated by simple computations involving components of the density matrix. Most importantly, they can be implemented in today's experiments by using at most O(n2)\mathcal{O}(n^2)O(n2) local measurements.
Abstract Quantum measurements based on mutually unbiased bases, mutually unbiased measurements and general symmetric informationally complete positive operator valued measurements, which are commonly used in quantum information and quantum computation. In this paper, by a broad class of informationally complete symmetric measurements and correlation matrices, some separability criteria are proposed for different quantum systems that are more robust and comprehensive than the corresponding criteria previously introduced L M Lai, T Li, S M Fei, and Z X Wang, (2018 Quantum Inf. Process., 17, 314); J W Shang, A Asadian, and H J Zhu, (2018 Phys. Rev. A 98, 022309). Furthermore, we extend the separability criteria of tripartite quantum systems to many-body systems. The proposed entanglement criteria may further enrich the relationship between quantum entanglement and measurement.
Quantum computers have the potentials to solve certain problems faster than classical computers. In quantum computer, entanglement is one of the elements beside superposition. Recently, with the advent of quantum information theory, entanglement has become an important resource for Quantum Information and Computation. The purpose of this paper is to discuss the separability criteria and method of measurement for entanglement. This paper is aimed at viewing the method that has been proposed in previous works in bipartite and multipartite entanglement. The outcome of this paper is to classify the different method that used to measure entanglement for bipartite and multipartite cases including the advantage and disadvantage of each method.
Abstract We study separability in arbitrary multipartite quantum systems based on principal base matrices. Necessary conditions are presented for different kinds of separable states. These conditions can give a complete classification of multipartite quantum states. While the usual Bloch representation of a density matrix uses three types of generators, the representation with principal base matrices has one uniform type of generator which simplifies computation. In this paper, we take advantage of this simplicity to derive useful and operational criteria to detect multipartite separability. We first obtain criteria on detecting 1 − 3 separable, 2 − 2 separable, 1 − 1 − 2 separable and fully separable four-partite quantum states. We then study k-separability for multipartite quantum states in arbitrary dimensions. Detailed examples are given to show that our criteria are able to detect more entanglement states than some existing criteria.