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Quantum states, maps, measurements a...

Kuah, Aik-Meng.

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Quantum states, maps, measurements and entanglement.

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Quantum states, maps, measurements and entanglement./
Author:	Kuah, Aik-Meng.
Description:	141 p.
Notes:	Adviser: E. C. G. Sudarshan.
Contained By:	Dissertation Abstracts International68-10B.
Subject:	Physics, Theory. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3285928
ISBN:	9780549266754

Quantum states, maps, measurements and entanglement.
Kuah, Aik-Meng.

Quantum states, maps, measurements and entanglement. - 141 p.

Adviser: E. C. G. Sudarshan.

Thesis (Ph.D.)--The University of Texas at Austin, 2007.

The structure of the set of density matrices, its linear transformations, generalized linear measurements, and entanglement are studied. The set of density matrices is shown to be a convex and stratified set with simplex and group symmetries. Generalized measurements for density matrices are shown to be reducible to one unitary transformation and one von Neumann measurement carried out with an ancillary system of fixed size. Linear maps of density matrices are considered and the volume of the set of maps is derived. Positive but not completely positive maps are studied in consideration of obtaining a test for entanglement in density matrices. Using the Jamiolkowski representation and Schmidt decomposition of the map eigen matrices, several properties of these maps are shown. An algebraic approach to constructing these positive but not completely positive maps is partially formulated.

ISBN: 9780549266754Subjects--Topical Terms:

1019422
Physics, Theory.

Quantum states, maps, measurements and entanglement.
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020 $a 9780549266754
035 $a (UMI)AAI3285928
035 $a AAI3285928
040 $a UMI $c UMI
100 1 $a Kuah, Aik-Meng. $3 1266249
245 1 0 $a Quantum states, maps, measurements and entanglement.
300 $a 141 p.
500 $a Adviser: E. C. G. Sudarshan.
500 $a Source: Dissertation Abstracts International, Volume: 68-10, Section: B, page: 6737.
502 $a Thesis (Ph.D.)--The University of Texas at Austin, 2007.
520 $a The structure of the set of density matrices, its linear transformations, generalized linear measurements, and entanglement are studied. The set of density matrices is shown to be a convex and stratified set with simplex and group symmetries. Generalized measurements for density matrices are shown to be reducible to one unitary transformation and one von Neumann measurement carried out with an ancillary system of fixed size. Linear maps of density matrices are considered and the volume of the set of maps is derived. Positive but not completely positive maps are studied in consideration of obtaining a test for entanglement in density matrices. Using the Jamiolkowski representation and Schmidt decomposition of the map eigen matrices, several properties of these maps are shown. An algebraic approach to constructing these positive but not completely positive maps is partially formulated.
520 $a The positivity of the linear map describing the evolution of an open system and its dependence on the initial state of the system is studied. For a system that is initialized to a zero-discord state, the evolution is shown to be given by a completely positive map. In quantum process tomography, the results obtained from a open system that is initially prepared using von Neumann measurements is shown to be described by a bi-linear map, not a linear map. A method for quantum process tomography is derived for qubit bi-linear maps. The difference between preparing states for an experiment by measurement and by stochastic process is analyzed, and it is shown that the two different methods will give fundamentally different outcomes.
590 $a School code: 0227.
650 4 $a Physics, Theory. $3 1019422
690 $a 0753
710 2 $a The University of Texas at Austin. $b Physics. $3 1018659
773 0 $t Dissertation Abstracts International $g 68-10B.
790 $a 0227
790 1 0 $a Sudarshan, E. C. G., $e advisor
791 $a Ph.D.
792 $a 2007
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3285928