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DOE OSTI · 22848449

Integrable nonlinear evolution of the qubit

Rembieliński, J.
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Abstract

Highlights: •We study the nonlinear generalization of the von Neumann equation. •We discuss the nonlinear von Neumann equation for the qubit states. •We analyze solutions to the Riccati system corresponding to evolution of a qubit. -- Abstract: The nonlinear generalization of the von Neumann equation is studied. The global version of this equation preserves convexity of the space of states. The particular case of the evolution of pure states refers to the nonlinear Schrödinger equation discovered by Gisin. The concrete realization of the nonlinear von Neumann equation is investigated in detail for the density matrix representing the qubit states. Such equation reduces to the integrable classical Riccati system of nonlinear ordinary differential equations. An interesting property of the nonlinear dynamics described by this system is the global asymptotical stability of stationary solutions related to evolution from mixed states to pure states.

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71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICSDENSITY MATRIXDIFFERENTIAL EQUATIONSMIXED STATEMIXED STATESNONLINEAR PROBLEMSPURE STATESQUANTUM MECHANICSQUBITSSTABILITY

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Rembieliński, J.. 2019-12-15. Integrable nonlinear evolution of the qubit. https://doi.org/10.1016/j.aop.2019.167955

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