Quantum Control and Representation Theory

Details Quantum Control and Representation Theory Quantum Control and Representation Theory

2012-03-11

arxiv.org/abs/1203.2380v1

J. Phys. A: Math. Theor., 42 205301-12 (2009)

Physics

Quantum Physics

Old paper, submitted for archival purposes

Scientific paper

A new notion of controllability for quantum systems that takes advantage of the linear superposition of quantum states is introduced. We call such notion von Neumann controllabilty and it is shown that it is strictly weaker than the usual notion of pure state and operator controlability. We provide a simple and effective characterization of it by using tools from the theory of unitary representations of Lie groups. In this sense we are able to approach the problem of control of quantum states from a new perspective, that of the theory of unitary representations of Lie groups. A few examples of physical interest and the particular instances of compact and nilpotent dynamical Lie groups are discussed.

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