Geometrical meaning of two-qubit entanglement and its symmetries

Geometrical meaning of two-qubit entanglement and its symmetries

Autor Braga, Helena Autor UNIFESP Google Scholar
Souza, Simone Autor UNIFESP Google Scholar
Mizrahi, Salomon S. Autor UNIFESP Google Scholar
Instituição Universidade Federal de São Paulo (UNIFESP)
Resumo For pure and mixed two-qubit states we present an analysis based on symmetries of vectors and matrices associated to the density operator. These symmetries are revealed by doing reflection operations on the vectors and the matrices by Cartesian planes. Then we consider states whose 4 x 4 matrices belong to the D-7 manifold class and introduce a new set of parameters. This procedure allows us to establish the Peres-Horodecki separability criterion in terms of a squared distance having a Minkowski metric. Thereafter, defining a phase space in terms of those parameters, we identify two regions, a cone and elsewhere. Separable states are represented by points located within the cone or on its surface (the border), while elsewhere the points stand for the entangled states. for a system evolving in time, if its state is initially entangled, then depending on the values of its parameters and on the nature of the interactions with the environment, the trajectory in the phase space may cross the border at a finite time, going from the entangledlike to the separablelike region and vice-versa. As a particular feature, crossings in one direction stand for the phenomenon of sudden death of entanglement, while crossings in the opposite direction hint for the sudden birth of entanglement. Our method dispenses with operations on the density matrix; it is sufficient to write the expressions directly in terms of matrix entries. Some illustrative examples are worked out.
Idioma Inglês
Financiador Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)
Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
Data de publicação 2010-04-01
Publicado em Physical Review A. College Pk: Amer Physical Soc, v. 81, n. 4, 8 p., 2010.
ISSN 1050-2947 (Sherpa/Romeo, fator de impacto)
Publicador Amer Physical Soc
Extensão 8
Direito de acesso Acesso restrito
Tipo Artigo
Web of Science WOS:000277227300044
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