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arXiv:quant-ph/0403205 · Physical Review A

Control of decoherence: Analysis and comparison of three different strategies

Paolo Facchi A, S. Tasaki, Saverio Pascazio, Hiromichi Nakazato, A. Tokuse, Daniel A. Lidar

Published Feb 8, 2005• 213 citations
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Abstract

We analyze and compare three different strategies, all aimed at controlling and eventually halting decoherence. The first strategy hinges upon the quantum Zeno effect, the second makes use of frequent unitary interruptions (``bang-bang'' pulses and their generalization, quantum dynamical decoupling), and the third uses a strong, continuous coupling. Decoherence is shown to be suppressed only if the frequency $N$ of the measurements or pulses is large enough or if the coupling $K$ is sufficiently strong. Otherwise, if $N$ or $K$ is large, but not extremely large, all these control procedures accelerate decoherence. We investigate the problem in a general setting and then consider some practical examples, relevant for quantum computation.

DOI
10.1103/physreva.71.022302

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We analyze and compare three different strategies, all aimed at controlling and eventually halting decoherence. The first strategy hinges upon the quantum Zeno effect, the second makes use of frequent unitary interruptions (``bang-bang'' pulses and their generalization, quantum dynamical decoupling), and the third uses a strong, continuous coupling. Decoherence is shown to be suppressed only if the frequency NNN of the measurements or pulses is large enough or if the coupling KKK is sufficiently strong. Otherwise, if NNN or KKK is large, but not extremely large, all these control procedures accelerate decoherence. We investigate the problem in a general setting and then consider some practical examples, relevant for quantum computation.
We discuss three control strategies, whose objective is to counter the effects of decoherence: the first strategy hinges upon the quantum Zeno effect, the second makes use of frequent unitary interruptions ("bang-bang" pulses), and the third of a strong, continuous coupling. Decoherence can be suppressed only if the frequency τ-1 of the measurements/pulses is large enough or if the coupling K is sufficiently strong. Otherwise, if τ-1 or K are large, but not sufficiently large, all these control procedures accelerate decoherence.
We discuss three control strategies, all aimed at countering the effects of deciherence. The first strategy hinges upon the quantum Zeno effect, the second makes use of frequent unitary interruptions ("bang-bang" pulses) and the third of a strong, continuous coupling. Decoherence is suppressed if the frequency N of the measurements/pulses is large enough or if the coupling K is sufficiently strong. However, if N or K are large, but not sufficiently large, all procedures accelerate decoherence.
We discuss three control strategies aimed at countering the effects of decoherence: the first hinges on frequent projective measurements, the second on frequent unitary "kicks" ("bang-bang" pulses) and the third on a strong continuous coupling. Decoherence is suppressed if the frequency N of the measurements/kicks is large enough or if the coupling K is sufficiently strong: in all these cases, the Hilbert space of the system splits into invariant subspaces, among which any transition is hindered. However, if N or K are large, but not extremely large, all these control procedures accelerate decoherence.
We unify the quantum Zeno effect (QZE) and the ``bang-bang'' (BB) decoupling method for suppressing decoherence in open quantum systems: in both cases strong coupling to an external system or apparatus induces a dynamical superselection rule that partitions the open system's Hilbert space into quantum Zeno subspaces. Our unification makes use of von Neumann' s ergodic theorem and avoids making any of the symmetry assumptions usually made in discussions of BB. Thus we are able to generalize the BB to arbitrary fast and strong pulse sequences, requiring no symmetry, and to show the existence of two alternatives to a pulsed BB: continuous decoupling and pulsed measurements. Our unified treatment enables us to derive limits on the efficacy of the BB method: we explicitly show that the inverse QZE implies that the BB can in some cases accelerate, rather than inhibit, decoherence.
The dynamics of a decohering two-level system driven by a suitable control Hamiltonian is studied. The control procedure is implemented as a sequence of radio-frequency pulses that repetitively flip the state of the system, a technique that can be termed quantum ``bang-bang'' control after its classical analog. Decoherence introduced by the system's interaction with a quantum environment is shown to be washed out completely in the limit of continuous flipping and greatly suppressed provided the interval between the pulses is made comparable to the correlation time of the environment. The model suggests a strategy to fight against decoherence that complements existing quantum error-correction techniques.
Abstract The control of thermal decoherence via dynamical decoupling and via the quantum Zeno effect (Zeno control) is investigated for a model of trapped ion, where the dynamics of two low‐lying hyperfine states undergoes decoherence due to the thermal interaction with an excited state. Dynamical decoupling is a procedure that consists in periodically driving the excited state, while the Zeno control consists in frequently measuring it. When the control frequency is high enough, decoherence is shown to be suppressed. Otherwise, both controls may accelerate decoherence. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004