Quantum phase estimation and realistic detection schemes in Mach-Zehnder interferometer using SU(2) coherent states

• URL: http://arxiv.org/abs/2412.20152v1
• Date: Sat, 28 Dec 2024 13:37:15 GMT
• Title: Quantum phase estimation and realistic detection schemes in Mach-Zehnder interferometer using SU(2) coherent states
• Authors: Mohammed Abdellaoui, Nour-Eddine Abouelkhir, Abdallah Slaoui, Rachid Ahl Laamara,
• Abstract summary: In quantum parameter estimation, the quantum Cram'er-Rao bound (QCRB) sets a fundamental limit on the precision achievable with unbiased estimators. We show that all three detection schemes can achieve the QCRB for the spin-coherent input state. We find that the best pressure is obtained when the total angular momentum quantum number $j$ is high.
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• Abstract: In quantum parameter estimation, the quantum Cram\'er-Rao bound (QCRB) sets a fundamental limit on the precision achievable with unbiased estimators. It relates the uncertainty in estimating a parameter to the inverse of the quantum Fisher information (QFI). Both QCRB and QFI are valuable tools for analyzing interferometric phase sensitivity. This paper compares the single-parameter and two-parameter QFI for a Mach-Zehnder interferometer (MZI) with three detection schemes: single-mode and difference intensity detection, neither has access to an external phase reference and balanced homodyne detection with access to an external phase reference. We use a spin-coherent state associated with the su(2) algebra as the input state in all scenarios and show that all three schemes can achieve the QCRB for the spin-coherent input state. Furthermore, we explore the utilization of SU(2) coherent states in diverse scenarios. Significantly, we find that the best pressure is obtained when the total angular momentum quantum number $j$ is high, and we demonstrate that given optimal conditions, all detection schemes can achieve the QCRB by utilizing SU(2) coherent states as input states.

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