Hidden Statistics of Schrödinger Equation

Work was carried out in determination of the mathematical origin of randomness in quantum mechanics and creating a hidden statistics of Schrödinger equation; i.e., to expose the transitional stochastic process as a “bridge” to the quantum world. The governing equations of hidden statistics would preserve such properties of quantum physics as superposition, entanglement, and direct-product decomposability while allowing one to measure its state variables using classical methods. In other words, such a system would reinforce the advantages and minimize the limitations of both quantum and classical aspects, and therefore, it will be useful for implementation of quantum computing.

Recent advances in quantum information theory have inspired an explosion of interest in new quantum algorithms for solving hard computational problems. Three basic “non-classical” properties of quantum mechanics — superposition, entanglement, and direct tensor-product decomposability — were main reasons for optimism about capabilities of quantum computers and quantum communications as well as for a new approach to cryptography. However, one major problem is keeping the components of a quantum computer in a coherent state, as the slightest interaction with the external world would cause the system to decohere. Another problem is measurement: by the laws of quantum mechanics, a measurement yields a random and incomplete answer, and it destroys the stored state.

This proposed reinterpretation of quantum formalism opens up new advantages of quantum computers: if the Madelung equations are implemented on a classical scale (using, for instance, electrical circuits or optical devices), all the quantum effects important for computations would be preserved; at the same time, the problems associated with decoherence and measurement would be removed.

This work was done by Michail Zak of Caltech for NASA’s Jet Propulsion Laboratory. For more information, contact This email address is being protected from spambots. You need JavaScript enabled to view it.. NPO-46731

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