Enhancing sensitivity in quantum metrology by Hamiltonian extensions

Julien Mathieu Elias Fraïsse and Daniel Braun
Phys. Rev. A 95, 062342 – Published 29 June 2017

Abstract

A well-studied scenario in quantum parameter estimation theory arises when the parameter to be estimated is imprinted on the initial state by a Hamiltonian of the form θG. For such “phase-shift Hamiltonians” it has been shown that one cannot improve the channel quantum Fisher information by adding ancillas and letting the system interact with them. Here we investigate the general case, where the Hamiltonian is not necessarily a phase shift, and show that in this case in general it is possible to increase the quantum channel information and to reach an upper bound. This can be done by adding a term proportional to the derivative of the Hamiltonian, or by subtracting a term from the original Hamiltonian. Neither method makes use of any ancillas, which shows that, for quantum channel estimation with an arbitrary parameter-dependent Hamiltonian, entanglement with an ancillary system is not necessary to reach the best possible sensitivity. By adding an operator to the Hamiltonian we can also modify the time scaling of the channel quantum Fisher information. We illustrate our techniques with nitrogen vacancy center magnetometry and the estimation of the direction of a magnetic field in a given plane using a single spin-1 as probe.

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  • Received 22 March 2017

DOI:https://doi.org/10.1103/PhysRevA.95.062342

©2017 American Physical Society

Physics Subject Headings (PhySH)

  1. Research Areas
Quantum Information, Science & Technology

Authors & Affiliations

Julien Mathieu Elias Fraïsse and Daniel Braun*

  • Eberhard-Karls-Universität Tübingen, Institut für Theoretische Physik, 72076 Tübingen, Germany

  • *daniel.braun@uni-tuebingen.de

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Issue

Vol. 95, Iss. 6 — June 2017

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