Bayesian quantum phase estimation with fixed photon states
arXiv:2308.01293 · doi:10.1007/s11128-024-04576-7
Abstract
We consider a two-mode bosonic state with fixed photon number , whose upper and lower modes pick up a phase and respectively. We compute the optimal Fock coefficients of the input state, such that the mean square error (MSE) for estimating is minimized while the minimum MSE is always attainable by a measurement. Our setting is Bayesian, i.e., we consider to be a random variable that follows a prior probability distribution function (PDF). Initially, we consider the flat prior PDF and we discuss the well-known fact that the MSE is not an informative tool for estimating a phase when the variance of the prior PDF is large. Therefore, we move on to study truncated versions of the flat prior in both single-shot and adaptive approaches. For our adaptive technique we consider and truncated prior PDFs. Each subsequent step utilizes as prior PDF the posterior probability of the previous step and at the same time we update the optimal state and optimal measurement.
Substantial additions on truncated flat prior probability density functions. Corrected a few typos. Cleaner presentation of new and previous results. Comments are welcome
References in corpus (32)
- Advances in Quantum Metrology
- Entanglement-free Heisenberg-limited phase estimation
- Optimal Quantum Phase Estimation
- Quantum Enhanced Multiple Phase Estimation
- Optimal states and almost optimal adaptive measurements for quantum interferometry
- Entanglement-enhanced measurement of a completely unknown phase
- A Geometric Perspective on Quantum Parameter Estimation
- Efficient Bayesian Phase Estimation
- How to perform the most accurate possible phase measurements
- Optimal quantum-enhanced interferometry using a laser power source
- True precision limits in quantum metrology
- A tradeoff in simultaneous quantum-limited phase and loss estimation in interferometry
- Ziv-Zakai Error Bounds for Quantum Parameter Estimation
- Phase estimation without a priori knowledge in the presence of loss
- Experimental estimation of one-parameter qubit gates in the presence of phase diffusion
- Bayesian quantum frequency estimation in presence of collective dephasing
- Bayesian multi-parameter quantum metrology with limited data
- Bayesian estimation of one-parameter qubit gates
- Quantum metrology in the presence of limited data
- Beyond quantum Fisher information: optimal phase estimation with arbitrary a priori knowledge
- Phase sensitivity bounds for two-mode interferometers
- Frequentist and Bayesian Quantum Phase Estimation
- Heisenberg-style bounds for arbitrary estimates of shift parameters including prior information
- Non-asymptotic analysis of quantum metrology protocols beyond the Cramér-Rao bound
- Atomtronic protocol designs for NOON states
- Bayesian parameter estimation using Gaussian states and measurements
- Quantum Weiss-Weinstein bounds for quantum metrology
- Designing optimal protocols in Bayesian quantum parameter estimation with higher-order operations
- Adaptive Bayesian phase estimation for quantum error correcting codes
- First-principles construction of symmetry-informed quantum metrologies
- Joint optimal measurement for locating two incoherent optical point sources near the Rayleigh distance
- Bayesian minimum mean square error for transmissivity sensing