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Phys. Rev. A 73, 052327 (2006) [6 pages]

Entangling power of the baker's map: Role of symmetries

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Rômulo F. Abreu and Raúl O. Vallejos
Centro Brasileiro de Pesquisas Físicas (CBPF), Rua Dr. Xavier Sigaud 150, 22290-180 Rio de Janeiro, Brazil

Received 28 March 2006; published 31 May 2006

Thequantum baker map possesses two symmetries: a canonical "spatial" symmetry,and a time-reversal symmetry. We show that, even when thesefeatures are taken into account, the asymptotic entangling power ofthe baker's map does not always agree with the predictionsof random matrix theory. We have verified that the dimensionof the Hilbert space is the crucial parameter that determineswhether the entangling properties of the baker map are universalor not. For power-of-2 dimensions, i.e., qubit systems, an anomalousentangling power is observed; otherwise the behavior of the bakermap is consistent with random matrix theories. We also derivea general formula that relates the asymptotic entangling power ofan arbitrary unitary with properties of its reduced eigenvectors.

©2006 The American Physical Society

URL:	http://link.aps.org/doi/10.1103/PhysRevA.73.052327
DOI:	10.1103/PhysRevA.73.052327
PACS:	03.67.Mn; 03.65.Ud; 03.65.Yz; 05.45.Mt 03.67.Mn Quantum entanglement production, characterization, and manipulation 03.65.Ud Entanglement and quantum nonlocality (e.g. EPR paradox, Bell's inequalities, GHZ states, etc.) 03.65.Yz Decoherence; open systems; quantum statistical methods 05.45.Mt Semiclassical methods in quantum chaos YEAR: 2006
KEYWORDS:	quantum entanglement, quantum computing, random processes, Hilbert spaces

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