Entanglement Detection by Local Orthogonal Observables

We propose a family of entanglement witnesses and corresponding positive maps that are not completely positive based on local orthogonal observables. As applications the entanglement witness of the $3\times 3$ bound entangled state [P. Horodecki, Phys. Lett. A {\bf 232}, 333 (1997)] is explicitly constructed and a family of $d$-dimensional bound entangled states is designed so that the entanglement can be detected by permuting local orthogonal observables. Further the proposed physically not implementable positive maps can be physically realized by measuring a Hermitian correlation matrix of local orthogonal observables.Comment: 4 pages, 1 figur

Bounds on the multipartite entanglement of superpositions

We derive the lower and upper bounds on the entanglement of a given multipartite superposition state in terms of the entanglement of the states being superposed. The first entanglement measure we use is the geometric measure, and the second is the q-squashed entanglement. These bounds allow us to estimate the amount of the multipartite entanglement of superpositions. We also show that two states of high fidelity to one another do not necessarily have nearly the same q-squashed entanglement.Comment: 4 pages, 2 figure. few typos correcte