Quantum Cones and Quantum Balls

Dosi, A.
The present note is dedicated to description of quantum systems among the quantum spaces. In the normed case we obtain a complete solution to the problem when an operator space turns out to be an operator system. The min and max quantizations of a local order are described in terms of the min and max envelopes of the related state spaces.


Quantum systems and representation theorem
Dosi, Anar (2013-09-01)
In this paper we investigate quantum systems which are locally convex versions of abstract operator systems. Our approach is based on the duality theory for unital quantum cones. We prove the unital bipolar theorem and provide a representation theorem for a quantum system being represented as a quantum -system.
Bipolar theorem for quantum cones
Dosi, A. (2012-09-01)
In this note duality properties of quantum cones are investigated. We propose a bipolar theorem for quantum cones, which provides a new proof of the operator bipolar theorem proved by Effros and Webster. In particular, a representation theorem for a quantum cone is proved.
Weight discrimination of boolean functions with quantum computation
Uyanık, Kıvanç; Turgut, Sadi; Department of Physics (2014)
In this thesis, we investigate solvability of the weight decision problem of two Boolean functions by quantum computation. In particular, we study this problem first from a general quantum operator discrimination perspective and second from a direct algorithmic viewpoint. As quantum operator discrimination approach is concerned, we give two different formulations for two different cases. In one, the unitary transformations that correspond to the function evaluation are applied in a parallel fashion and in t...
Dosi, Anar (2011-06-01)
In the note we investigate the main duality properties of quantum (or local operator) spaces involving quantum homology. Namely, we prove that each finite complete homology admits precisely one quantization and each complete quantum space is a matrix homology quotient of a local trace class algebra.
Does Quantum Mechanics Select Out Regularity and Local Mode Behaviour in Nonlinearly Coupled Vibrational Systems?
Yurtsever, E.; Brickmann, J. (Wiley, 1990-8)
A two dimensional strongly nonharmonic vibrational system with nonlinear intermode coupling is studied both classically and quantum mechanically. The system was chosen such that there is a low lying transition (in energy) from a region where almost all trajectories move regularly to a region where chaotic dynamics strongly dominates. The corresponding quantum system is far away from the semiclassical limit. The eigenfunctions are calculated with high precision according to a linear variational scheme using ...
Citation Formats
A. Dosi, “Quantum Cones and Quantum Balls,” AZERBAIJAN JOURNAL OF MATHEMATICS, pp. 142–151, 2018, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/64291.