Variational principle for optimal quantum controls in quantum metrology
- URL: http://arxiv.org/abs/2111.04117v2
- Date: Tue, 26 Apr 2022 06:41:54 GMT
- Title: Variational principle for optimal quantum controls in quantum metrology
- Authors: Jing Yang, Shengshi Pang, Zekai Chen, Andrew N. Jordan, and Adolfo del
Campo
- Abstract summary: We develop a variational principle to determine the quantum controls and initial state which optimize the quantum Fisher information.
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.
- Score: 2.29042212865183
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: We develop a variational principle to determine the quantum controls and
initial state which 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 the 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.
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