Quantum systems and representation theorem

Dosi, Anar
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.


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...
Quantum system structures of quantum spaces and entanglement breaking maps
Dosi, A. A. (IOP Publishing, 2019-07-01)
This paper is devoted to the classification 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. Finally, we characterize min-max-completely positive maps between Archimedean order unit spaces and investigate entanglement breaking maps in the general setting of quantum...
Quantum duality, unbounded operators, and inductive limits
Dosi, Anar (AIP Publishing, 2010-06-01)
In this paper, we investigate the inductive limits of quantum normed (or operator) spaces. This construction allows us to treat the space of all noncommutative continuous functions over a quantum domain as a quantum (or local operator) space of all matrix continuous linear operators equipped with G-quantum topology. In particular, we classify all quantizations of the polynormed topologies compatible with the given duality proposing a noncommutative Arens-Mackey theorem. Further, the inductive limits of oper...
Environmental effects on quantum geometric phase and quantum entanglement
Günhan, Ali Can; Pak, Namık Kemal; Department of Physics (2008)
We investigate the geometric phase (GP) acquired by the states of a spin-1/2 nucleus which is subject to a static magnetic field. This nucleus as the carrier system of GP, is taken as coupled to a dissipative environment, so that it evolves non-unitarily. We study the effects of different characteristics of different environments on GP as nucleus evolves in time. We showed that magnetic field strength is the primary physical parameter that determines the stability of GP; its stability decreases as the magne...
Spin–orbit effects on the nonlinear optical properties of a quantum dot in simultaneous electric and magnetic fields
Aytekin, O.; Turgut, Sadi; Tomak, Mehmet (Elsevier BV, 2014-11)
We report on the nonlinear optical properties of a quantum dot including the Rashba spin-orbit interaction (RSOI) with external electric and magnetic fields. The effect of dot size is considered. We do not make any assumptions about the strength of the confinement. We use the numerical diagonalization of the Hamiltonian to determine the electronic structure. The confining potential is taken to be of the Woods-Saxon type. We find the effect of RSOI on nonlinear optical coefficients.
Citation Formats
A. Dosi, “Quantum systems and representation theorem,” POSITIVITY, pp. 841–861, 2013, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/63730.