2007/10/31 by Yeong-Cherng Liang, Lluís Masanes, Andrew C. Doherty
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.77.012332
published as Physical Review A, vol. 77, art. 012332 (2008) · 8 pages, 3 figures; this is Ref.[13] in eprint quant-ph/0703268. Changes made since last version: typos in Eq (5) corrected; Fig 2 and Fig 3 replaced; references updated
openalex publication_date 2008/01/25 · arxiv created 2008/03/06 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
In this paper we classify the four-qubit states that commute with U\ensuremath\bigotimesU\ensuremath\bigotimesV\ensuremath\bigotimesV, where U and V are arbitrary members of the Pauli group. We characterize the set of separable states for this class, in terms of a finite number of entanglement witnesses. Equivalently, we characterize the two-qubit, Bell-diagonal-preserving, completely positive maps that are separable. These separable completely positive maps correspond to protocols that can be implemented with stochastic local operations assisted by classical communication (SLOCC). This allows us to derive a complete set of SLOCC monotones for Bell-diagonal states, which, in turn, provides the necessary and sufficient conditions for converting one two-qubit state to another by SLOCC.