Deterministic Transformations of Multipartite Entangled States with Tensor Rank 2

Transformations involving only local operations assisted with classical communication are investigated for multipartite entangled pure states having tensor rank 2. All necessary and sufficient conditions for the possibility of deterministically converting truly multipartite, rank-2 states into each other are given. Furthermore, a chain of local operations that successfully achieves the transformation has been identified for all allowed transformations. The identified chains have two nice features: (1) each party needs to carry out at most one local operation and (2) all of these local operations are also deterministic transformations by themselves. Finally, it is found that there are disjoint classes of states, all of which can be identified by a single real parameter, which remain invariant under deterministic transformations.Comment: 27 pages, 1 figure; added new references and improved the presentatio

Elastic wave cloaking via symmetrized transformation media

Transformation media theory, which steers waves in solids via an effective geometry induced by a refractive material (Fermat's principle of least action), provides a means of controlling vibrations and elastic waves beyond the traditional dissipative structures regime. In particular, it could be used to create an elastic wave cloak, shielding an interior region against elastic waves while simultaneously preventing scattering in the outside domain. However, as a true elastic wave cloak would generally require nonphysical materials with stiffness tensors lacking the minor symmetry (implying asymmetric stress), the utility of such an elastic wave cloak has thus far been limited. Here we develop a means of overcoming this limitation via the development of a symmetrized elastic cloak, sacrificing some of the performance of the perfect cloak for the sake of restoring the minor symmetry. We test the performance of the symmetrized elastic cloak for shielding a tunnel against seismic waves, showing that it can be used to reduce the average displacement within the tunnel by an order of magnitude (and reduce energy by two orders of magnitude) for waves above a critical frequency of the cloak. This critical frequency, which corresponds to the generation of surface waves at the cloak-interior interface, can be used to develop a simple heuristic model of the symmetrized elastic cloak's performance for a generic problem