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Phase space methods in finite quantum systems.

By Hilal Al Hadhrami

Abstract

Quantum systems with finite Hilbert space where position x and momentum\ud p take values in Z(d) (integers modulo d) are considered. Symplectic tranformations\ud S(2¿,Z(p)) in ¿-partite finite quantum systems are studied and\ud constructed explicitly. Examples of applying such simple method is given\ud for the case of bi-partite and tri-partite systems. The quantum correlations\ud between the sub-systems after applying these transformations are discussed\ud and quantified using various methods. An extended phase-space x¿p¿X¿P\ud where X, P ¿ Z(d) are position increment and momentum increment, is introduced.\ud In this phase space the extended Wigner and Weyl functions are\ud defined and their marginal properties are studied. The fourth order interference\ud in the extended phase space is studied and verified using the extended\ud Wigner function. It is seen that for both pure and mixed states the fourth\ud order interference can be obtained.Ministry of Higher Education, Sultanate of Oma

Topics: Phase space methods, Finite quantum systems, Finite Hilbert space, Symplectic tranformations, Bi-partite and tri-partite systems, Wigner function
Publisher: Department of Computing
Year: 2009
OAI identifier: oai:bradscholars.brad.ac.uk:10454/4250
Provided by: Bradford Scholars

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