论文信息 - Algorithm for Quantum-like Representation: Transformation of Probabilistic Data into Vectors on Bloch's Sphere

Algorithm for Quantum-like Representation: Transformation of Probabilistic Data into Vectors on Bloch's Sphere

In this paper, we present a simple algorithm for representation of statis-tical data of any origin by complex probability amplitudes. Numerical simulation withMathematica-6 is performed, cf. [1] and [2] on recent numerical simulation for quantumcorrelations. The Bloch's sphere is used for the visualization of results of numerical sim-ulation. On the one hand, creation of such a quantum-like (QL) representation and itsnumerical approval is an important step in clari¯cation of extremely complicated inter-relation between classical and quantum randomness. On the other hand, it opens newpossibilities for applying the mathematical formalism of QM in other domains of science.

Andrei Khrennikov

[1] Olga V. Man'ko,et al. Quantum states in probability representation and tomography , 1997 .

[2] Emmanuel Haven. A Black-Scholes Schrödinger option price: ‘bit’ versus ‘qubit’ , 2003 .

[3] Andrei Khrennikov. Interference of probabilities and number field structure of quantum models , 2001 .

[4] Emmanuel Haven,et al. A discussion on embedding the Black-Scholes option pricing model in a quantum physics setting , 2002 .

[5] Andrei Khrennikov,et al. The Principle of Supplementarity: A Contextual Probabilistic Viewpoint to Complementarity, the Interference of Probabilities and Incompatibility of Variables in Quantum Mechanics , 2005 .

[6] G M D'Ariano,et al. Toward a tomographic picture of a Bose-Einstein condensate. , 2000, Journal of the Optical Society of America. A, Optics, image science, and vision.

[7] K. Michielsen,et al. A local realist model for correlations of the singlet state , 2006 .

[8] Kristel Michielsen,et al. A computer program to simulate Einstein-Podolsky-Rosen-Bohm experiments with photons , 2007, Comput. Phys. Commun..