The equivalence of multipartite quantum mixed states under local unitary transformations is studied. A criterion for the equivalence of non-degenerate mixed multipartite quantum states under local unitary transformations is presented. PACS numbers: 03.67.-a, 02.20.Hj, 03.65.-w Quantum entangled states are playing fundmental roles in quantum information processing such as quantum computation, quantum teleportation, dense coding, quantum cryptographic schemes quantum error correction, entanglement swapping, and remote state preparation (RSP) etc.. However the theory of quantum entanglement is still far from being satisfied. To quantify the degree of entanglement a number of entanglement measures have been proposed for bipartite states. Most of these proposed measures of entanglement involve extremizations which are difficult to handle analytically. For multipartite case how to give a well defined measure is still under discussion. For general mixed states till now we don’t even have an operational criterion to verify whether a state is separable or not. As a matter

As the Netflix Prize competition has demonstrated, matrix factorization models are superior to classic nearest-neighbor techniques for producing product recommendations, allowing the incorporation of additional information such as implicit feedback, temporal effects, and confidence levels. Modern

signals. We prove that there is no point in making the number of transmitter antennas greater than the length of the coherence interval: the capacity for M> Tis equal to the capacity for M = T. Capacity is achieved when the T M transmitted signal matrix is equal to the product of two statistically

This paper describes an approach for the automatic generation and optimization of numerical software for processors with deep memory hierarchies and pipelined functional units. The production of such software for machines ranging from desktop workstations to embedded processors can be a tedious

As a contribution to the project for recognising matrix groups defined over finite fields, we describe an algorithm for deciding whether or not the natural module for such a matrix group can be decomposed into a non-trivial tensor product. In the affirmative case, a tensor decomposition

. In this work, we bridge the gap between the two approaches and introduce the compressed sparse fiber (CSF) a data structure for sparse tensors along with a novel par-allel algorithm for tensor-matrix multiplication. CSF offers similar operation reductions as existing compressed methods while using only a

The production of thematic maps, such as those depicting land cover, using an image classification is one of the most common applications of remote sensing. Considerable research has been directed at the various components of the mapping process, including the assessment of accuracy. This paper

Abstract. A symmetric tensor is a higher order generalization of a symmetric matrix. In this paper, we study various properties of symmetric tensors in relation to a decomposition into a symmetric sum of outer product of vectors. A rank-1 order-k tensor is the outer product of k non-zero vectors

By an embedding approach and through tensor products, some inequalities for generalized matrix functions (of positive semidefinite matrices) associated with any subgroup of the permutation group and any irreducible character of the subgroup are obtained.

and their relationships. Index Terms—Design structure matrix, information flow, inte-gration analysis, modularity, organization design, product archi-tecture, product development, project management, project plan-ning, scheduling, systems engineering. I.