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Title: Classification scheme of pure multipartite states based on topological phases
Authors: Johansson, M.
Ericsson, M.
Sjöqvist, E. 
Osterloh, A.
Issue Date: 21-Jan-2014
Citation: Johansson, M., Ericsson, M., Sjöqvist, E., Osterloh, A. (2014-01-21). Classification scheme of pure multipartite states based on topological phases. Physical Review A - Atomic, Molecular, and Optical Physics 89 (1) : -. ScholarBank@NUS Repository.
Abstract: We investigate the connection between the concept of affine balancedness (a-balancedness) introduced by M. Johansson et al. [Phys. Rev. A 85, 032112 (2012)1050-2947PLRAAN10.1103/PhysRevA.85.032112] and polynomial local SU invariants and the appearance of topological phases, respectively. It is found that different types of a-balancedness correspond to different types of local SU invariants analogously to how different types of balancedness, as defined by A. Osterloh and J. Siewert, [New J. Phys. 12, 075025 (2010)1367-2630NJOPFM10.1088/ 1367-2630/12/7/075025], correspond to different types of local special linear (SL) invariants. These different types of SU invariants distinguish between states exhibiting different topological phases. In the case of three qubits, the different kinds of topological phases are fully distinguished by the three-tangle together with one more invariant. Using this, we present a qualitative classification scheme based on balancedness of a state. While balancedness and local SL invariants of bidegree (2n,0) classify the SL-semistable states [A. Osterloh and J. Siewert, New J. Phys. 12, 075025 (2010)NJOPFM1367-263010.1088/1367-2630/12/7/075025; O. Viehmann, Phys. Rev. A 83, 052330 (2011)1050-2947PLRAAN10.1103/PhysRevA.83.052330], a-balancedness and local SU invariants of bidegree (2n-m,m) give a more fine-grained classification. In this scheme, the a-balanced states form a bridge from the genuine entanglement of balanced states, invariant under the SL group, towards the entanglement of unbalanced states characterized by U invariants of bidegree (n,n). As a byproduct, we obtain generalizations to the W state, i.e., states that are entangled, but contain only globally distributed entanglement of parts of the system. © 2014 American Physical Society.
Source Title: Physical Review A - Atomic, Molecular, and Optical Physics
ISSN: 10502947
DOI: 10.1103/PhysRevA.89.012320
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