Tensor Rank and Entanglement Transformation between Multipartite Pure States
Cheng Guo, Tsinghua University & University of Technology, Sydney
The tensor rank of a symmetric tensor is equal to the polynomial rank of some homogeneous polynomial. I will introduce the isomorphism between symmetric states and homogeneous polynomials. I will also present recent results in this research area, i.e., polynomial rank of a monomial, polynomial rank of reducible cubic forms, and tensor rank of multi-copy W state and asymptotic entanglement transformation rate from GHZ state to W state via stochastic local operations and classical communication.
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