Adaptive estimation of a time-varying phase with a power-law spectrum via continuous squeezed states

Abstract

When measuring a time-varying phase, the standard quantum limit and Heisenberg limit as usually defined, for a constant phase, do not apply. If the phase has Gaussian statistics and a power-law spectrum $1/|\omega {|}^p$ with $p>1$, then the generalized standard quantum limit and Heisenberg limit have recently been found to have scalings of $1/{\mathcal{N}}^{(p-1)/p}$ and $1/{\mathcal{N}}^{2(p-1)/(p+1)}$, respectively, where $\mathcal{N}$ is the mean photon flux. We show that this Heisenberg scaling can be achieved via adaptive measurements on squeezed states. We predict the experimental parameters analytically, and test them with numerical simulations. Previous work had considered the special case of $p=2$.

arXiv comment11 pages, comments welcome

References in corpus (25)

• Detection of 15 dB Squeezed States of Light and their Application for the Absolute Calibration of Photoelectric Quantum Efficiency
• Quantum Metrology with Two-Mode Squeezed Vacuum: Parity Detection Beats the Heisenberg Limit
• Adaptive homodyne measurement of optical phase
• General optimality of the Heisenberg limit for quantum metrology
• Quantum-enhanced optical phase tracking
• Ab-initio Quantum Enhanced Optical Phase Estimation Using Real-time Feedback Control
• Ziv-Zakai Error Bounds for Quantum Parameter Estimation
• Adaptive Optical Phase Estimation Using Time-Symmetric Quantum Smoothing
• Sub-Heisenberg estimation strategies are ineffective
• The quantum Bell-Ziv-Zakai bounds and Heisenberg limits for waveform estimation
• Does nonlinear metrology offer improved resolution? Answers from quantum information theory
• Adaptive Quantum Measurements of a Continuously Varying Phase
• Universality of the Heisenberg limit for estimates of random phase shifts
• Quantum measurement bounds beyond the uncertainty relations
• Bayesian estimation in homodyne interferometry
• Sub-Heisenberg estimation of non-random phase-shifts
• Optimal Heisenberg-style bounds for the average performance of arbitrary phase estimates
• Stochastic Heisenberg limit: Optimal estimation of a fluctuating phase
• Adaptive phase measurements for narrowband squeezed beams
• Unbounded quantum Fisher information in two-path interferometry with finite photon number
• Adaptive phase estimation is more accurate than non-adaptive phase estimation for continuous beams of light
• Alternative measures of uncertainty in quantum metrology: Contradictions and limits
• Phase measurements at the theoretical limit
• Signal detection without finite-energy limits to quantum resolution
• Optimal waveform estimation for classical and quantum systems via time-symmetric smoothing

Cited by in corpus (4)

• Standard Quantum Limit and Heisenberg Limit in Function Estimation
• Quantum-enhanced stochastic phase estimation with SU(1,1) interferometer
• Adaptive estimation of a time-varying phase with coherent states: smoothing can give an unbounded improvement over filtering
• Quantum enhanced optical phase estimation with a squeezed thermal state