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Physics of Particles and Nuclei Letters

Entangled solitons and stochastic q-bits

Yu. P. Rybakov, T. F. Kamalov

Published Mar 1, 2007• 3 citations
Publisher

Abstract

Stochastic realization of the wave function in quantum mechanics with the inclusion of soliton representation of extended particles is discussed. Two-soliton configurations are used for constructing entangled states in generalized quantum mechanics dealing with extended particles, endowed with nontrivial spin S. Entangled solitons construction being introduced in the nonlinear spinor field model, the Einstein-Podolsky-Rosen (EPR) correlation is calculated and shown to coincide with the quantum mechanical one for the 1/2-spin particles. The concept of stochastic qubits is used for quantum computing modeling.

DOI
10.1134/s1547477107020033

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Stochastic realization of the wave function in quantum mechanics with the inclusion of soliton representation of extended particles is discussed. Two-soliton configurations are used for constructing entangled states in generalized quantum mechanics dealing with extended particles, endowed with nontrivial spin S. Entangled solitons construction being introduced in the nonlinear spinor field model, the Einstein-Podolsky-Rosen (EPR) correlation is calculated and shown to coincide with the quantum mechanical one for the 1/2-spin particles. The concept of stochastic qubits is used for quantum computing modeling.
Special stochastic representation of the wave function in Quantum Mechanics (QM), based on soliton realization of extended particles, is suggested with the aim to model quantum states via classical computer. Entangled solitons construction being introduced in the nonlinear spinor field model, the Einstein, Podolsky, Rosen (EPR) spin correlation is calculated and shown to coincide with the quantum mechanical one for the spin-1/2 particles in the singlet state. The concept of stochastic qubits is used for quantum computing modelling.
Starting with the projective interpretation of the Hilbert space special stochastic representation of the wave function in Quantum Mechanics (QM), based on soliton realization of extended particles, is considered with the aim to model quantum states via classical computer. Entangled solitons construction having been earlier introduced in the nonlinear spinor field model for the calculation of the Einstein-Podolsky-Rosen (EPR) spin correlation for the spin-1/2 particles in the singlet state, the other example is now studied. The latter concerns the entangled envelope solitons in Kerr dielectric with cubic nonlinearity, where we use two-solitons configurations for modeling the entangled states of photons. Finally, the concept of stochastic qubits is used for quantum computing modeling.
Background Using the Einstein's idea on particles-solitons, the stochastic representation of the wave function as a large sum of solitons with random phases is suggested.Purpose To illustrate the main idea of the stochastic representation, let us recall the lectures by N. Wiener on nonlinear problems in random theory.Method In these lectures Wiener used the so-called 𝛼-representation of the wave function for a nonrelativistic particle in three-dimensional space, the wave function being considered as an element of the random Hilbert space with the Gaussian dispersion.Results This representation appears to be equivalent, in accordance with the central limiting theorem, to the sum of many complex solitons with random phases.Conclusions On the basis of this representation it is possible to substantiate the Born's rule for measuring physical observables and also to explain the "spin-statistics" correlation in quantum mechanics.
This extended note deals with a pedagogical description of the entangled state of two particles, starting from first principles. After some general remarks about quantum mechanics and physical theories, the single particle case is discussed by defining state, uncertainty relations and wave function in the state space. The system of two particles is then considered, with its possible states, starting from the original papers by Einstein Podolsky Rosen and by Schroedinger. The quantum measurement problem is then introduced, together with its role in the entanglement state. Finally the orthodox solution and the relevant conclusions are drawn.
Two solitons in a nonlinear fiber behave like two particles. They propagate without distortion, collide elastically gaining quantum correlations and emerge separately from the fiber providing the condition of spacelike separation. The entanglement appearing between positions and momenta of the two distanced solitons allows us a close following of the famous Einstein-Podolsky-Rosen (EPR) reasoning with two correlated quantum particles. The particlelike behavior of the solitons makes our proposal conceptually different from the previous optical schemes with correlated plane waves (photons).