[en] We develop a variational principle to determine the quantum controls and initial state that optimizes the quantum Fisher information, the quantity characterizing the precision in quantum metrology. When the set of available controls is limited, the exact optimal initial state and the optimal controls are, in general, dependent on the probe time, a feature missing in the unrestricted case. Yet, for time-independent Hamiltonians with restricted controls, the problem can be approximately reduced to the unconstrained case via Floquet engineering. In particular, we find for magnetometry with a time-independent spin chain containing three-body interactions, even when the controls are restricted to one- and two-body interaction, that the Heisenberg scaling can still be approximately achieved. Our results open the door to investigate quantum metrology under a limited set of available controls, of relevance to many-body quantum metrology in realistic scenarios.
Disciplines :
Physics
Author, co-author :
YANG, Jing ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Physics and Materials Science (DPHYMS)
Pang, Shengshi; School of Physics, Sun Yat-Sen University, Guangzhou, Guangdong 510275, China
Chen, Zekai; Department of Physics and Astronomy, University of Rochester, Rochester, New York 14627, USA
Jordan, Andrew N.; Institute for Quantum Studies, Chapman University, 1 University Drive, Orange, California 92866, USA ; Department of Physics and Astronomy, University of Rochester, Rochester, New York 14627, USA
DEL CAMPO ECHEVARRIA, Adolfo ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Physics and Materials Science (DPHYMS)
External co-authors :
yes
Language :
English
Title :
Variational principle for optimal quantum controls in quantum metrology
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This is the approach pursued in, e.g., the variational approach in shortcut to adiabaticity [26,27]. Another way of handling the constraints on the control Hamiltonian is by introducing the following constraints (Equation presented), (Equation presented) to disallow the terms (Equation presented), where (Equation presented). This way of introducing the constraint is the one used in, e.g., a quantum brachistochrone equation [21,22]. However, in many-body quantum metrology, the number of disallowed nonlocal operators is much more than the allowed local operators. Therefore, the second approach may introduce an intractable number of constraints and we shall pursue the first approach of expanding (Equation presented) in terms of basis operators in the main text.
We choose the normalization (Equation presented) to all orders of (Equation presented), which is different from the normalization (Equation presented) used in Refs. [33,36]. Therefore, the resulting expression of (Equation presented) is different from the one in Refs. [33,36], up to some irrelevant constant, which does not affect the form of the Floquet effective Hamiltonian (Equation presented).
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