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Paper 1

Locally inequivalent four qubit hypergraph states

Xiao-yu Chen, Lei Wang

Year

2014

Journal

arXiv preprint

DOI

arXiv:1409.0928

arXiv

1409.0928

Hypergraph states as real equally weighted pure states are important resources for quantum codes of non-local stabilizer. Using local Pauli equivalence and permutational symmetry, we reduce the 32768 four qubit real equally weighted pure states to 28 locally inequivalent hypergraph states and several graph states. The calculation of geometric entanglement supplemented with entanglement entropy confirms that further reduction is impossible for true hypergraph states.

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Paper 2

Systematic Construction of Genuine Multipartite Entanglement Criteria using Uncertainty Relations

A. Saboia, A. T. Avelar, S. P. Walborn, F. Toscano

Year

2014

Journal

arXiv preprint

DOI

arXiv:1407.7248

arXiv

1407.7248

A general procedure to construct criteria for identifying genuine multipartite continuous variable entanglement is presented. It relies on the proper definition of adequate global operators describing the multipartite system, the positive partial transpose criterion of separability, and quantum mechanical uncertainty relations. As a consequence, each criterion encountered consists of a single inequality that is nicely computable and experimentally feasible, and that when violated is sufficient condition for genuine multipartite entanglement. Additionally we show that the previous work of van Loock and Furusawa [Phys. Rev. A, 67, 052315 (2003)] is a special case of our result that includes strongest criteria to detect entanglement.

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