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Physical Review A

Control of the quantum open system via quantum generalized measurement

Ming Zhang, Hong‐Yi Dai, Xiaocai Zhu, Xing-Wei Li, Dewen Hu

Published Mar 3, 2006• 26 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.73.032101

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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.
This paper demonstrates that the decoherence-free subsystem of open quantum dynamical system is open-loop controllable if the suitable coherent controls are permitted. This result is in marked contrast to the fact that open quantum dynamical systems are not open-loop controllable. In other words, combining the decoherence-free subsystem condition with coherent control on the open quantum dynamical systems will enhance the ability to suppress the decoherence and to manipulate open quantum dynamical systems.
We propose the concept of the quantum generalized projector measurement (QGPM) for finite-dimensional quantum systems by studying the quantum generalized measurement. This research reveals a distinguished property of this quantum generalized measurement: no matter what the system state is prior to the measurement and what the result of the measurement occurs, the state of the system after the measurement can be collapsed into any specified pure state, i.e., the state of quantum system can be deterministically reduced to any specified pure state just by a single QGPM. Subsequently, QGPM can be used to deterministically generate the maximum entangled pure state for quantum systems. We give three concrete theoretic schemes of generating the maximum quantum entangled pure states for two 2-level particles, three 2-level particles and two 3-level particles, respectively.
We propose the concept of the quantum generalized subspace projector measurement (QGSPM). The distinguished properties of QGSPM is revealed: no matter what the state of the system is prior to the measurement and what the measured result occurs, the state posterior to the measurement can be collapsed onto the specified subspace. Subsequently, the quantum generalized case-projector measurement (QGCPM), as a special case of QGSPM, is also discussed carefully. It is demonstrated that no matter what measured result occurs, the state of the system posterior to QGCPM can be collapsed into one of pure states. Consequently, QGCPM can be used to generate the maximally entangled pure states for multiple particles. As illustrative examples, several concrete methods of generating entanglement are proposed for two two-level particles. It is found that the maximally entangled pure states of two 2-level particles can be generated just by a single QGCPM and the corresponding QGCPM operators are physically realizable in principle if an ancillary four-dimensional quantum system can be introduced.
Abstract A common objective for quantum control is to force a quantum system, initially in an unknown state, into a particular target subspace. We show that if the subspace is required to be a decoherence-free subspace of dimension greater than 1, then such control must be decoherent. That is, it will take almost any pure state to a mixed state. We make no assumptions about the control mechanism, but our result implies that for this purpose coherent control offers no advantage, in principle, over the obvious measurement-based feedback protocol.
This paper discusses the concept of controllable subspace for open quantum dynamical systems.It is constructively demonstrated that combining structural features of decoherence-free subspaces with the ability to perform open-loop coherent control on open quantum systems will allow decoherence-free subspaces to be controllable.This is in contrast to the observation that open quantum dynamical systems are not open-loop controllable.To a certain extent, this paper gives an alternative control theoretical interpretation on why decoherence-free subspaces can be useful for quantum computation.
We propose a method to overcome phase damping decoherence by periodically performing open loop tracking control and generalized measurement. Although it is impossible to stabilize a qubit subject to Markovian dynamics only by open loop coherent control, one can attain a dasiasoftenedpsila control goal with the help of periodical generalized measurement. The dasiasoftenedpsila control objective in our scheme is to keep the state of the controlled qubit to stay near a reference pure state all the time. Two sub-optimal control problems are given in the sense of trace distance and fidelity, respectively, and they are eventually reduced to the choice of a period T.