Multipartite entanglement constitutes one of the key resources in quantum information processing. We exploit correlation tensor norms to develop a framework for its experimental detection without the need for shared frames of reference. By bounding these norms for partially separable states and states of limited dimension, we achieve an extensive characterization of entanglement in multipartite systems in an experimentally feasible way. Furthermore, we show that both bi- and multipartite dimensionality of entanglement can be revealed by our methods.
Multipartite quantum correlations, in spite of years of intensive research, still leave many questions unanswered. While bipartite entanglement is relatively well understood for Gaussian states, the complexity of mere qualitative characterization grows rapidly with increasing number of parties. Here, we present two schemes for transformations of multipartite permutation invariant Gaussian states by Gaussian local operations and classical communication. To this end, we use a scheme for possible experimental realization, making use of the fact that in this picture the whole
N-partite state can be described by specifying the states of two separable modes. Numerically, we study entanglement transformations of tripartite states. Finally, we look at the effect our protocols have on fidelity of assisted quantum teleportation and find that, while adding correlated noise does not affect the fidelity at all, there is strong evidence that partial nondemolition measurement leads to a drop in teleportation fidelity.
A characterization of multipartite quantum states having
N subsystems, based on negativities of matrices obtained by selective partial transposition of the state operator, is proposed. The
K-way partial transpose with respect to a subsystem is constructed by imposing constraints involving the states of
K subsystems of the multipartite composite system. The
K-way negativity, defined as the negativity of
K-way partial transpose, quantifies the
K-way coherences of the composite system. For an
N-partite system the fraction of
K-way negativity $(2\ensuremath{\le}K\ensuremath{\le}N)$, contributing to global negativity, is obtained. The entanglement measures for a given state $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\rho}}$ are identified as the partial
K-way negativities of the corresponding canonical state.