2009/10/24 by Nengkun Yu, Eric Chitambar, Cheng Guo +1 · 1 citation
Computer Science · Physics and Astronomy · #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #quant-ph
paper · pdf · doi:10.1103/physreva.81.014301
published as Phys. Rev. A 81, 014301 (2010) · Comments: 3 pages (Revtex 4). Minor corrections to Theorem 1. Presentation refined. Main results unchanged. Comments are welcome
arxiv created 2009/10/24 · openalex publication_date 2010/01/15 · arxiv updated 2013/09/24 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
Tensor rank refers to the number of product states needed to express a given multipartite quantum state. Its nonadditivity as an entanglement measure has recently been observed. In this Brief Report, we estimate the tensor rank of multiple copies of the tripartite state |W\ensuremath⟩=(1)/(√(3))(|100\ensuremath⟩+|010\ensuremath⟩+|001\ensuremath⟩). Both an upper bound and a lower bound of this rank are derived. In particular, it is proven that the rank of |W\ensuremath⟩^\ensuremath\bigotimes2 is 7, thus resolving a previously open problem. Some implications of this result are discussed in terms of transformation rates between |W\ensuremath⟩^\ensuremath\bigotimesn and multiple copies of the state |GHZ\ensuremath⟩=(1)/(√(2))(|000\ensuremath⟩+|111\ensuremath⟩).