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arXiv:quant-ph/0610191 · Physical Review A

Indirect control with a quantum accessor: Coherent control of multilevel system via a qubit chain

H. C. Fu, Hui Dong, Xingfang Liu, Che Sun

Published May 14, 2007• 18 citations
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Abstract

The indirect controllability of an arbitrary finite-dimensional quantum system ($N$-dimensional qudit) through a quantum accessor is investigated. Here, the qudit is coupled to a quantum accessor, which is modeled as a fully controllable spin chain with nearest-neighbor (anisotropic) $XY$ coupling. The complete controllability of such an indirect control system is investigated in detail. The general approach is applied to the indirect controllability of two- and three-dimensional quantum systems. For two- and three-dimensional systems, a simpler indirect control scheme is also presented.

DOI
10.1103/physreva.75.052317

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arXiv:1203.0887•Mar 5, 2012•0 citations
The indirect controllability of an arbitrary finite-dimensional quantum system (NNN-dimensional qudit) through a quantum accessor is investigated. Here, the qudit is coupled to a quantum accessor, which is modeled as a fully controllable spin chain with nearest-neighbor (anisotropic) XYXYXY coupling. The complete controllability of such an indirect control system is investigated in detail. The general approach is applied to the indirect controllability of two- and three-dimensional quantum systems. For two- and three-dimensional systems, a simpler indirect control scheme is also presented.
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.
A pure indirect control of quantum systems via a 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 two- and three-dimensional systems. The scheme exhibits some advantages; it uses less qubits in the accessor and does not depend on the energy-level structure of the controlled system.
This is the second one in our series of papers on indirect quantum control assisted by quantum accessor. In this paper we propose and study a new class of indirect quantum control(IDQC) scheme based on the initial states preparation of the accessor. In the present scheme, after the initial state of the accessor is properly prepared, the system is controlled by repeatedly switching on and off the interaction between the system and the accessor. This is different from the protocol of our first paper, where we manipulate the interaction between the controlled system and the accessor. We prove the controllability of the controlled system for the proposed indirect control scheme. Furthermore, we give an example with two coupled spins qubits to illustrate the scheme, the concrete control process and the controllability.
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.
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.