Obtain W-state from three-qubit GHZ-state on rate 1

Original · EN

In this paper, we study the entanglement transformation rate between multipartite states under stochastic local operations and classical communication (SLOCC). Firstly, we show that the entanglement transformation rate from GHZ=1√2(000+111) to W=1√3(100+010+001) is 1, that is, one can obtain 1 copy of W-state, from 1 copy of GHZ-state by SLOCC, asymptotically. We then generalize this result to a lower bound on the rate that from N-partite GHZ-state to Dicke states. For some special cases, the optimality of this bound is proved. We then discuss the tensor rank of matrix permanent by evaluating the the tensor rank of Dicke state.