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arXiv · 1304.6275

Relationship among locally maximally entanglable states, W states and hypergraph states under local unitary transformations

Ri Qu·Yi-ping Ma·Bo Wang·Yan-ru Bao
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Abstract

Kruszynska and Kraus [Phys. Rev. A 79, 052304 (2009)] have recently introduced the so-called locally maximally entanglable (LME) states of n qubits which can be maximally entangled to local auxiliary qubits using controlled operations. We characterize the local entanglability of hypergraph states and W states using an approach in [Phys. Rev. A 79, 052304 (2009)]. We show that (i) all hypergraph states are LME; (ii) hypergraph states and LME states are not equivalent under local unitaries; (iii) a W state of n qubits is not LME; and (iv) no hypergraph state of n qubits can be converted into to the W state under local unitary transformations. Moreover, we also present an approach for encoding weighted hypergraphs into LME states.

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Ri Qu, Yi-ping Ma, Bo Wang, Yan-ru Bao. 2013-05-03. Relationship among locally maximally entanglable states, W states and hypergraph states under local unitary transformations. https://doi.org/10.1103/physreva.87.052331

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