Quantum control of a single qubit

Agata M. Brańczyk, Paulo E. M. F. Mendonça, Alexei Gilchrist, Andrew C. Doherty, and Stephen D. Bartlett
Phys. Rev. A 75, 012329 – Published 24 January 2007

Abstract

Measurements in quantum mechanics cannot perfectly distinguish all states and necessarily disturb the measured system. We present and analyze a proposal to demonstrate fundamental limits on quantum control of a single qubit arising from these properties of quantum measurements. We consider a qubit prepared in one of two nonorthogonal states and subsequently subjected to dephasing noise. The task is to use measurement and feedback control to attempt to correct the state of the qubit. We demonstrate that projective measurements are not optimal for this task, and that there exists a nonprojective measurement with an optimum measurement strength which achieves the best trade-off between gaining information about the system and disturbing it through measurement backaction. We study the performance of a quantum control scheme that makes use of this weak measurement followed by feedback control, and demonstrate that it realizes the optimal recovery from noise for this system. We contrast this approach with various classically inspired control schemes.

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  • Received 15 August 2006

DOI:https://doi.org/10.1103/PhysRevA.75.012329

©2007 American Physical Society

Authors & Affiliations

Agata M. Brańczyk1, Paulo E. M. F. Mendonça1, Alexei Gilchrist1, Andrew C. Doherty1, and Stephen D. Bartlett2

  • 1Department of Physics, The University of Queensland, Queensland 4072, Australia
  • 2School of Physics, The University of Sydney, New South Wales 2006, Australia

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Vol. 75, Iss. 1 — January 2007

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