Descriptions of quadratic plus linear operators which preserve pure states of the quantum system
As we knew, a mathematical formalism of a quantum mechanics says that any quantum system is identified with some finite- or infinite-dimensional Hilbert space; pure states correspond to vectors of norm 1; observables are self-adjoint operators on the space of states. Thus the set of all pure stat...
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2013
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| Online Access: | http://irep.iium.edu.my/33661/ http://irep.iium.edu.my/33661/1/Paper_for_IREP.pdf |
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iium-336612014-01-06T03:48:33Z http://irep.iium.edu.my/33661/ Descriptions of quadratic plus linear operators which preserve pure states of the quantum system Saburov, Mansoor QA Mathematics As we knew, a mathematical formalism of a quantum mechanics says that any quantum system is identified with some finite- or infinite-dimensional Hilbert space; pure states correspond to vectors of norm 1; observables are self-adjoint operators on the space of states. Thus the set of all pure states corresponds to the unit sphere in the Hilbert space [1-2]. It is of interest to describe all linear or nonlinear operators which preserve the pure states of the system. In the linear case, it is nothing more than isometries of Hilbert spaces [1]. In the nonlinear case, this problem was open. In this paper we shall describe all quadratic plus linear operators which preserve pure states of the quantum system.! 2013-12-03 Conference or Workshop Item PeerReviewed application/pdf en http://irep.iium.edu.my/33661/1/Paper_for_IREP.pdf Saburov, Mansoor (2013) Descriptions of quadratic plus linear operators which preserve pure states of the quantum system. In: International Conference on Quantum Optics and Quantum Information (icQoQi 2013), 3-5 Dec. 2013, Bukit Gambang Resort City, Pahang, Malaysia. |
| repository_type |
Digital Repository |
| institution_category |
Local University |
| institution |
International Islamic University Malaysia |
| building |
IIUM Repository |
| collection |
Online Access |
| language |
English |
| topic |
QA Mathematics |
| spellingShingle |
QA Mathematics Saburov, Mansoor Descriptions of quadratic plus linear operators which preserve pure states of the quantum system |
| description |
As we knew, a mathematical formalism of a quantum mechanics says that any quantum system is
identified with some finite- or infinite-dimensional Hilbert space; pure states correspond to vectors
of norm 1; observables are self-adjoint operators on the space of states. Thus the set of all pure
states corresponds to the unit sphere in the Hilbert space [1-2]. It is of interest to describe all linear
or nonlinear operators which preserve the pure states of the system. In the linear case, it is nothing
more than isometries of Hilbert spaces [1]. In the nonlinear case, this problem was open. In this
paper we shall describe all quadratic plus linear operators which preserve pure states of the
quantum system.! |
| format |
Conference or Workshop Item |
| author |
Saburov, Mansoor |
| author_facet |
Saburov, Mansoor |
| author_sort |
Saburov, Mansoor |
| title |
Descriptions of quadratic plus linear operators which preserve pure states of the quantum system |
| title_short |
Descriptions of quadratic plus linear operators which preserve pure states of the quantum system |
| title_full |
Descriptions of quadratic plus linear operators which preserve pure states of the quantum system |
| title_fullStr |
Descriptions of quadratic plus linear operators which preserve pure states of the quantum system |
| title_full_unstemmed |
Descriptions of quadratic plus linear operators which preserve pure states of the quantum system |
| title_sort |
descriptions of quadratic plus linear operators which preserve pure states of the quantum system |
| publishDate |
2013 |
| url |
http://irep.iium.edu.my/33661/ http://irep.iium.edu.my/33661/1/Paper_for_IREP.pdf |
| first_indexed |
2023-09-18T20:48:40Z |
| last_indexed |
2023-09-18T20:48:40Z |
| _version_ |
1777409846511927296 |