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Title: Lorentz singular-value decomposition and its applications to pure states of three qubits
Authors: Verstraete, Frank ×
Dehaene, Jeroen
De Moor, Bart #
Issue Date: Mar-2002
Publisher: American physical soc
Series Title: Physical Review A, Atomic, Molecular and Optical Physics vol:65 pages:032308
Abstract: All mixed states of two qubits can be brought into normal form by the action of local operations and classical communication operations of the kind rho'=(AxB) rho(AxB)dagger. These normal forms can be obtained by considering a Lorentz singular-value decomposition on a real parametrization of the density matrix. We show that the Lorentz singular values are variationally defined and give rise to entanglement monotones, with as a special case the concurrence. Next a necessary and sufficient criterion is conjectured for a mixed state to be convertible into another specific one with a nonzero probability. Finally the formalism of the Lorentz singular-value decomposition is applied to tripartite pure states of qubits. New proofs are given for the existence of the Greenberger-Horne-Zeilinger (GHZ) class and W class of states, and a rigorous proof for the optimal distillation of a GHZ state is derived.
URI: 
ISSN: 1050-2947
Publication status: published
KU Leuven publication type: IT
Appears in Collections:ESAT - STADIUS, Stadius Centre for Dynamical Systems, Signal Processing and Data Analytics
Tutorial services, Faculty of Engineering
× corresponding author
# (joint) last author

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