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arXiv · 0806.4701

Basics of Quantum Mechanics, Geometrization and some Applications to Quantum Information

J. Clemente-Gallardo·G. Marmo
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Abstract

In this paper we present a survey of the use of differential geometric formalisms to describe Quantum Mechanics. We analyze Schrödinger framework from this perspective and provide a description of the Weyl-Wigner construction. Finally, after reviewing the basics of the geometric formulation of quantum mechanics, we apply the methods presented to the most interesting cases of finite dimensional Hilbert spaces: those of two, three and four level systems (one qubit, one qutrit and two qubit systems). As a more practical application, we discuss the advantages that the geometric formulation of quantum mechanics can provide us with in the study of situations as the functional independence of entanglement witnesses.

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J. Clemente-Gallardo, G. Marmo. 2008-06-28. Basics of Quantum Mechanics, Geometrization and some Applications to Quantum Information. https://doi.org/10.1142/s0219887808003156

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