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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| Format: | Proceeding Paper |
| Language: | English |
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2013
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| Online Access: | http://irep.iium.edu.my/33661/1/Paper_for_IREP.pdf |
| _version_ | 1796878423371546624 |
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| author | Saburov, Mansoor |
| author_facet | Saburov, Mansoor |
| author_sort | Saburov, Mansoor |
| collection | IIUM |
| 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.! |
| first_indexed | 2024-03-05T23:21:16Z |
| format | Proceeding Paper |
| id | oai:generic.eprints.org:33661 |
| institution | International Islamic University Malaysia |
| language | English |
| last_indexed | 2024-03-05T23:21:16Z |
| publishDate | 2013 |
| record_format | dspace |
| spelling | oai:generic.eprints.org: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 Proceeding Paper 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. |
| spellingShingle | QA Mathematics Saburov, Mansoor Descriptions of quadratic plus linear operators which preserve pure states of the quantum system |
| title | 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_short | 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 |
| topic | QA Mathematics |
| url | http://irep.iium.edu.my/33661/1/Paper_for_IREP.pdf |
| work_keys_str_mv | AT saburovmansoor descriptionsofquadraticpluslinearoperatorswhichpreservepurestatesofthequantumsystem |