title: Obtaining a W state from a Greenberger-Horne-Zeilinger state via stochastic local operations and classical communication with a rate approaching unity.
abstract: We introduce a notion of the entanglement transformation rate to characterize the asymptotic comparability of two multipartite pure entangled states under stochastic local operations and classical communication (SLOCC). For two well known SLOCC inequivalent three-qubit states |GHZ⟩=(1/2)(|000⟩+|111⟩) and |W⟩=(1/3)(|100⟩+|010⟩+|001⟩), we show that the entanglement transformation rate from |GHZ⟩ to |W⟩ is exactly 1. That means that we can obtain one copy of the W state from one copy of the Greenberg-Horne-Zeilinger (GHZ) state by SLOCC, asymptotically. We then apply similar techniques to obtain a lower bound on the entanglement transformation rates from an N-partite GHZ state to a class of Dicke states, and prove the tightness of this bound for some special cases which naturally generalize the |W⟩ state. A new lower bound on the tensor rank of the matrix permanent is also obtained by evaluating the tensor rank of Dicke states.
authors.affiliation: State Key Laboratory of Intelligent Technology and Systems, Tsinghua National Laboratory for Information Science and Technology, Department of Computer Science and Technology, Tsinghua University, Beijing 100084, China and Centre for Quantum Computation and Intelligent Systems (QCIS), Faculty of Engineering and Information Technology, University of Technology, Sydney (UTS), New South Wales 2007, Australia.
authors.forename: Nengkun
authors.initials: N
authors.lastname: Yu
authors.affiliation: Centre for Quantum Computation and Intelligent Systems (QCIS), Faculty of Engineering and Information Technology, University of Technology, Sydney (UTS), New South Wales 2007, Australia.
authors.forename: Cheng
authors.initials: C
authors.lastname: Guo
authors.affiliation: State Key Laboratory of Intelligent Technology and Systems, Tsinghua National Laboratory for Information Science and Technology, Department of Computer Science and Technology, Tsinghua University, Beijing 100084, China and Centre for Quantum Computation and Intelligent Systems (QCIS), Faculty of Engineering and Information Technology, University of Technology, Sydney (UTS), New South Wales 2007, Australia and UTS-AMSS Joint Research Laboratory for Quantum Computation and Quantum Information Processing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China.
authors.forename: Runyao
authors.initials: R
authors.lastname: Duan