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Quantum control in infinite dimensions. (English) Zbl 1118.81378

Summary: Accurate control of quantum evolution is an essential requirement for quantum state engineering, laser chemistry, quantum information and quantum computing. Conditions of controllability for systems with a finite number of energy levels have been extensively studied. By contrast, results for controllability in infinite dimensions have been mostly negative, stating that full control cannot be achieved with a finite-dimensional control Lie algebra. Here we show that by adding a discrete operation to a Lie algebra it is possible to obtain full control in infinite dimensions with a small number of control operators.

MSC:

81Q99 General mathematical topics and methods in quantum theory
81P68 Quantum computation
93B05 Controllability
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References:

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