Quantum metrology in a lossless Mach-Zehnder interferometer using entangled photon inputs

• URL: http://arxiv.org/abs/2310.02049v1
• Date: Tue, 3 Oct 2023 13:43:02 GMT
• Title: Quantum metrology in a lossless Mach-Zehnder interferometer using entangled photon inputs
• Authors: Shreyas Sadugol and Lev Kaplan
• Abstract summary: We estimate the phase uncertainty in a noiseless Mach-Zehnder interferometer using photon-counting detection. We first devise an estimation and measurement strategy that yields the lowest phase uncertainty for a single measurement.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Using multi-photon entangled input states, we estimate the phase uncertainty in a noiseless Mach-Zehnder interferometer (MZI) using photon-counting detection. We assume a flat prior uncertainty and use Bayesian inference to construct a posterior uncertainty. By minimizing the posterior variance to get the optimal input states, we first devise an estimation and measurement strategy that yields the lowest phase uncertainty for a single measurement. N00N and Gaussian states are determined to be optimal in certain regimes. We then generalize to a sequence of repeated measurements, using non-adaptive and fully adaptive measurements. N00N and Gaussian input states are close to optimal in these cases as well, and optimal analytical formulae are developed. Using these formulae as inputs, a general scaling formula is obtained, which shows how many shots it would take on average to reduce phase uncertainty to a target level. Finally, these theoretical results are compared with a Monte Carlo simulation using frequentist inference. In both methods of inference, the local non-adaptive method is shown to be the most effective practical method to reduce phase uncertainty.

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