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k-separability criterion of mixed multipartite quantum states

Ting Gao, Yan Hong

Published Apr 13, 2012• 2 citations
OpenAlex

Abstract

The $k$-separability of mixed $n$-partite ($n\geq 3$) quantum states is mainly discussed in this paper. We obtain practical $k$-separability criteria to identify $k$-nonseparable mixed multipartite states in arbitrary dimensional quantum systems and detect genuine $n$-partite entanglement ($k=2$) and entanglement ($k=3$) which have previously not been identified. No optimization or eigenvalue evaluation is needed, our criteria can be evaluated by simple computations involving components of the density matrix and can be implemented in today's experiments.

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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.
Detection of kkk-nonseparable nnn-partite quantum states
The detection of multipartite entanglement in arbitrary dimensional systems is investigated. We derive useful kkk-separability criteria of mixed nnn-partite (n≥3n\geq 3n≥3) quantum states to detect kkk-nonseparable nnn-partite quantum states. Our criteria can be expressed by the elements of the density matrix, which allows a simple and practical evaluation and computation. They are experimentally accessible without quantum state tomography.
We investigate the detection of entanglement in nnn-partite quantum states. We obtain practical separability criteria to identify genuinely entangled and nonseparable mixed quantum states. No numerical optimization or eigenvalue evaluation is needed, and our criteria can be evaluated by simple computations involving components of the density matrix. We provide examples in which our criteria perform better than all known separability criteria. Specifically, we are able to detect genuine nnn-partite entanglement which has previously not been identified. In addition, our criteria can be used in today's experiments.
We derive a general framework to identify genuinely multipartite entangled mixed quantum states in arbitrary-dimensional systems and show in exemplary cases that the constructed criteria are stronger than those previously known. Our criteria are simple functions of the given quantum state and detect genuine multipartite entanglement that had not been identified so far. They are experimentally accessible without quantum state tomography and are easily computable as no optimization or eigenvalue evaluation is needed.
The kkk-nonseparability is a kind of multipartite quantum correlation which can be used to characterize some aspects of multipartite entanglement. In this paper, we discuss the detection of kkk-nonseparability of nnn-partite quantum states from an information perspective and obtain some kkk-nonseparability criteria in terms of quantum Fisher information. These criteria can identify many kkk-nonseparable states, and their advantages over an important and well-known kkk-nonseparability criterion [M. Huber et al., Phys. Rev. A 88, 042328 (2013)] are illustrated by several typical examples.
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.