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arXiv:0807.1384

Indirect control of quantum system via accessor: pure coherent control without system excitation

H. C. Fu, Hui Dong, X. F. Liu, Chuan Sun

Published Jul 9, 2008• 1 citation
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Abstract

A pure indirect control of quantum systems via quantum accessor is investigated. In this control scheme, we do not apply any external classical excitation fields on the controlled system and we control a quantum system via a quantum accessor and classical control fields control the accessor only. Complete controllability is investigated for arbitrary finite dimensional quantum systems and exemplified by 2 and 3 dimensional systems. The scheme exhibits some advantages; it uses less qubits in accessor and does not depend on the energy-level structure of the controlled system.

DOI
10.48550/arxiv.0807.1384

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A pure indirect control of quantum systems via quantum accessor is investigated. In this control scheme, we do not apply any external classical excitation fields on the controlled system and we control a quantum system via a quantum accessor and classical control fields control the accessor only. Complete controllability is investigated for arbitrary finite dimensional quantum systems and exemplified by 2 and 3 dimensional systems. The scheme exhibits some advantages; it uses less qubits in accessor and does not depend on the energy-level structure of the controlled system.
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In coherent feedback control schemes a target quantum system S is put in contact with an auxiliary system A and the coherent control can directly affect only A. The system S is controlled indirectly through the interaction with A. The system S is said to be indirectly controllable if every unitary transformation can be performed on the state of S with this scheme. In this paper we show how indirect controllability of S is equivalent to complete controllability of the combined system S + A, if the dimension of A is ≥ 3. In the case where the dimension of A is equal to 2, it is possible to have indirect controllability without having complete controllability of S +A and we give sufficient conditions for this to happen. We conjecture that these conditions are also necessary. The results of the paper extend the result of [5] and expand the results of [6] to systems of arbitrary dimensions.
A quantum mechanical system S is indirectly controlled when the control affects an ancillary system A and the evolution of S is modified through the interaction with A only. A study of indirect controllability gives a description of the set of states that can be obtained for S with this scheme. In this paper, we study the indirect controllability of quantum systems in the finite dimensional case. After discussing the relevant definitions, we give a general necessary condition for controllability in Lie algebraic terms. We present a detailed treatment of the case where both systems, S and A, are two-dimensional (qubits). In particular, we characterize the dynamical Lie algebra associated with S+A, extending previous results, and prove that complete controllability of S+A and an appropriate notion of indirect controllability are equivalent properties for this system. We also prove several further indirect controllability properties for the system of two qubits, and illustrate the role of the Lie algebraic analysis in the study of reachable states.