Relationship among locally maximally entangleable states, W states, and hypergraph states under local unitary transformations
Ri Qu, Yi-Ping Ma, Bo Wang, Yan-ru Bao · Physical Review A · 2013
Kruszynska and Kraus [Phys. Rev. A 79, 052304 (2009)] have recently introduced the so-called locally maximally entangleable (LME) states of $n$ qubits which can be maximally entangled with local auxiliary qubits using controlled operations. We characterize the local entangleability of hypergraph states and $W$ states using the approach of Kruszynska and Kraus. 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 the $W$ state under local unitary transformations. Moreover, we also present an approach for encoding weighted hypergraphs into LME states.