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Physical Review A

Control of the quantum open system via quantum generalized measurement (5 pages)

M. Zhang, Xiaobo Zhu, Hui Dai

Published Jan 1, 2006• 0 citations
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Control of the quantum open system via quantum generalized measurement

Ming Zhang, Hong‐Yi Dai, Xiaocai Zhu +2 more

For any specified pure state of quantum open system, we can construct a kind of quantum generalized measurement (QGM) that the state of the system after measurement will be deterministically collapsed into the specified pure state from any initial state. In other words, any pure state of quantum open system is reachable by QGM. Subsequently, whether the qubit is density matrix controllable is discussed in the case of pure dephasing. Our results reveal that combining QGM with coherent control will enhance the ability of controlling the quantum open system. Furthermore, it is found that the ability to perform QGM on the quantum open system, combined with the ability of coherence control and conditions of decoherence-free subspace, allows us to suppress quantum decoherence.

Physical Review A•Mar 3, 2006•26 citations

Generalized Controllability of Quantum Systems: Beyond the Limitation of Open-loop Controllability

Ming Zhang, Dewen Hu, Hong‐Yi Dai +1 more

To control a quantum system, not only may an ancillary system be introduced, but unitary operations and quantum projective measurement can also be performed on the quantum system or the resulting composite system. As a quantum system may be "physically" controllable even if the quantum system is not open-loop controllable, it is, therefore, necessary to go beyond the limitation of open-loop controllability for quantum systems. By studying the link between quantum generalized measurement and generalized pure state reachability, we further clarify the rationality of redefining the concept of generalized controllability from a view point of physical operation. It is also demonstrated that applying unitary operations, performing quantum projective measurement and introducing ancillary systems can play important roles in controlling quantum systems. Therefore, instead of adopting the concept of open-loop controllability for quantum systems, we need to define and discuss the concept of generalized controllability from a view point of physical operation. This is in marked contrast to the fact that the "physical" controllability for classical systems can only be discussed in the sense of open- loop control.

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Measurement, filtering and control in quantum open dynamical systems

V. P. Belavkin

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For any specified pure state of quantum open system, we can construct a kind of quantum generalized measurement (QGM) that the state of the system after measurement will be deterministically collapsed into the specified pure state from any initial state. In other words, any pure state of quantum open system is reachable by QGM. Subsequently, whether the qubit is density matrix controllable is discussed in the case of pure dephasing. Our results reveal that combining QGM with coherent control will enhance the ability of controlling the quantum open system. Furthermore, it is found that the ability to perform QGM on the quantum open system, combined with the ability of coherence control and conditions of decoherence-free subspace, allows us to suppress quantum decoherence.
To control a quantum system, not only may an ancillary system be introduced, but unitary operations and quantum projective measurement can also be performed on the quantum system or the resulting composite system. As a quantum system may be "physically" controllable even if the quantum system is not open-loop controllable, it is, therefore, necessary to go beyond the limitation of open-loop controllability for quantum systems. By studying the link between quantum generalized measurement and generalized pure state reachability, we further clarify the rationality of redefining the concept of generalized controllability from a view point of physical operation. It is also demonstrated that applying unitary operations, performing quantum projective measurement and introducing ancillary systems can play important roles in controlling quantum systems. Therefore, instead of adopting the concept of open-loop controllability for quantum systems, we need to define and discuss the concept of generalized controllability from a view point of physical operation. This is in marked contrast to the fact that the "physical" controllability for classical systems can only be discussed in the sense of open- loop control.