Minimal-noise estimation of noncommuting rotations of a spin

• URL: http://arxiv.org/abs/2303.08591v3
• Date: Tue, 16 Apr 2024 17:28:08 GMT
• Title: Minimal-noise estimation of noncommuting rotations of a spin
• Authors: Jakub Czartowski, Karol Życzkowski, Daniel Braun,
• Abstract summary: We propose an analogue of $textSU (1,1)$ interferometry to measure rotation of a spin by using two-spin squeezed states. For a specific direction and strength an advantage in sensitivity for all equatorial rotation axes over the classical bound is shown. Our results provide a method for measuring magnetic fields in any direction in the $x$-$y$-plane with the same optimized initial state.
• Score: 0.9217021281095907
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We propose an analogue of $\text{SU}(1,1)$ interferometry to measure rotation of a spin by using two-spin squeezed states. Attainability of the Heisenberg limit for the estimation of the rotation angle is demonstrated for maximal squeezing. For a specific direction and strength an advantage in sensitivity for all equatorial rotation axes (and hence non-commuting rotations) over the classical bound is shown in terms of quadratic scaling of the single-parameter quantum Fisher information for the corresponding rotation angles. Our results provide a method for measuring magnetic fields in any direction in the $x$-$y$-plane with the same optimized initial state.

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