1Doctoral School of Exact and Natural Sciences, Jagiellonian University, ul. Łojasiewicza 11, 30-348 Kraków, Poland
2Faculty of Physics, Astronomy and Applied Computer Science, Jagiellonian University, ul. Łojasiewicza 11, 30-348 Kraków, Poland
3Centrum Fizyki Teoretycznej PAN, Al. Lotników 32/46, 02-668 Warszawa, Poland
4National Quantum Information Center (KCIK), University of Gdańsk, Poland
5Institute of Theoretical Physics, University of Tübingen, Auf der Morgenstelle 14, 72076 Tübingen, Germany
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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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Cited by
[1] R. J. Lewis-Swan, J. C. Zuñiga Castro, D. Barberena, and A. M. Rey, “Exploiting Nonclassical Motion of a Trapped Ion Crystal for Quantum-Enhanced Metrology of Global and Differential Spin Rotations”, Physical Review Letters 132 16, 163601 (2024).
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