Enhancing sensitivity in quantum metrology by Hamiltonian extensions

Enhancing sensitivity in quantum metrology by Hamiltonian extensions 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Physical Review A American Physical Society (APS)

Enhancing sensitivity in quantum metrology by Hamiltonian extensions

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Enhancing sensitivity in quantum metrology by Hamiltonian extensions

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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Publisher
The American Physical Society
Copyright
Copyright © ©2017 American Physical Society
ISSN
1050-2947
eISSN
1094-1622
D.O.I.
10.1103/PhysRevA.95.062342
Publisher site
See Article on Publisher Site

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.

Journal

Physical Review AAmerican Physical Society (APS)

Published: Jun 29, 2017

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