arXiv subjects

Alexander M. Soiguine

Publications and source records attributed to Alexander M. Soiguine.

4 recordsLinked to original sources

arXiv2015

Quantum state evolution in C2 and G3+

It was shown that quantum mechanical qubit states as elements of two dimensional complex space can be generalized to elements of even subalgebra of geometric (Clifford) algebra over Euclidian space. The construction critically depends on generalization of formal, unspecified, complex plane to arbitrary variable, but explicitly defined, planes in 3D, and of usual Hopf fibration to maps generated by arbitrary unit value bivectors. Analysis of the new structure demonstrates that quantum state evolution in terms of two dimensional complex space gives only restricted information compared to that in even geometric algebra.

physics.gen-ph↗

arXiv2015

Geometric algebra, qubits, geometric evolution, and all that

The earlier approach is used for description of qubits and geometric phase parameters, the things critical in the area of topological quantum computing. The used tool, Geometric (Clifford) Algebra is the most convenient formalism for that case. Generalization of formal complex plane to an an arbitrary plane in three dimensions and of usual Hopf fibration to the map generated by an arbitrary unit value element of even sub-algebra of the three-dimensional Geometric Algebra are resulting in more profound description of qubits compared to quantum mechanical Hilbert space formalism.

physics.gen-ph↗

arXiv2014

A tossed coin as quantum mechanical object

Comprehensive and physically consistent model of a tossed coin is presented in terms of geometric algebra. The model clearly shows that there is nothing elementary particle specific in the half-spin quantum mechanical formalism. It also demonstrates what really is behind this formalism, feasibly reveals the probabilistic meaning of wave function and shows that arithmetic of packed objects, namely wave functions and Pauli matrices, reduces the amount of available information.

physics.gen-ph↗

arXiv2014

What quantum state really is?

To get out of logical deadlock in interpreting gedanken experiments like Schrodinger cat, actual meaning of a wave function, or a state, in the case of complex two-dimensional Hilbert space, is shown to represent transformations executing by elements of even subalgebra of geometric algebra over three-dimensional Euclidian space.

physics.gen-ph↗