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arXiv:1204.2864 · Europhysics Letters (EPL)

Efficient k-separability criteria for mixed multipartite quantum states

Ting Gao, Yan Hong, Yao Lu, Fengli Yan

Published Oct 1, 2013• 49 citations
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Abstract

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.

DOI
10.1209/0295-5075/104/20007

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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.
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