Speaker

   Dr. Lin Chen, Institute for Quantum Computing, University of Waterloo, Canada  

　　Title

  Symmetric tensor rank, homogeneous polynomial rank and multipartite entangled states under stochastic-LOCC              

　　Time

    2013.7.11 10:00-11:00am                                      

　　Venue

　　S712

　　Abstract

    The tensor rank (also known as generalized Schmidt rank) of multipartite pure states plays an important role in the study of entanglement classifications and transformations. We employ powerful tools from the theory of homogeneous polynomials to investigate the tensor rank of symmetric states such as the tripartite state |W_3>=1/√3(|100>+|010>+|001>) and its N-partite generalization |W_N>. Previous tensor rank estimates are dramatically improved and we show that (i) three copies of |W_3> have a rank of either 15 or 16, (ii) two copies of |W_N> have a rank of 3N-2, and (iii) n copies of |W_N> have a rank of O(N). A remarkable consequence of these results is that certain multipartite transformations, impossible even probabilistically, can become possible when performed in multiple-copy bunches or when assisted by some catalyzing state. This effect is impossible for bipartite pure states.

　　Affiliation