Fisher information of a squeezed-state interferometer with a finite photon-number resolution

Abstract

Squeezed-state interferometry plays an important role in quantum-enhanced optical phase estimation, as it allows the estimation precision to be improved up to the Heisenberg limit by using ideal photon-number-resolving detectors at the output ports. Here we show that for each individual $N$-photon component of the phase-matched coherent $\otimes$ squeezed vacuum input state, the classical Fisher information always saturates the quantum Fisher information. Moreover, the total Fisher information is the sum of the contributions from each individual $N$-photon components, where the largest $N$ is limited by the finite number resolution of available photon counters. Based on this observation, we provide an approximate analytical formula that quantifies the amount of lost information due to the finite photon number resolution, e.g., given the mean photon number $\bar{n}$ in the input state, over $96$ percent of the Heisenberg limit can be achieved with the number resolution larger than $5\bar{n}$.

A new analytical result of the Fisher information (Eq.(18), or more generally, Eq.(B9)) has been derived to quantify how much the phase information is kept (or lost) due to finite number resolution of the photon-counting detectors

References in corpus (18)

• Quantum Optical Metrology -- The Lowdown on High-N00N States
• Optimal Quantum Phase Estimation
• Observation of squeezed light with 10dB quantum noise reduction
• Mach-Zehnder Interferometry at the Heisenberg Limit with coherent and squeezed-vacuum light
• Fisher information under decoherence in Bloch representation
• An avalanche-photodiode-based photon-number-resolving detector
• Quantum Metrological Limits via a Variational Approach
• Phase detection at the quantum limit with multi-photon Mach-Zehnder interferometry
• All path-symmetric pure states achieve their maximal phase sensitivity in conventional two-path interferometry
• Generation of Large Number-Path Entanglement Using Linear Optics and Feed-Forward
• High photon number path entanglement in the interference of spontaneously downconverted photon pairs with coherent laser light
• Optimal Quantum-Enhanced Interferometry
• Optical interferometry in the presence of large phase diffusion
• Quantum-limited metrology in the presence of collisional dephasing
• Quantum interferometry with binary-outcome measurements in the presence of phase diffusion
• Heisenberg-limited metrology with information recycling
• Analytical formula for numerical evaluations of the Wigner rotation matrices at high spins
• Conditionally generating a mesoscopic superposition of N00N states

Cited by in corpus (3)

• Practical resources and measurements for lossy optical quantum metrology
• Data processing over single-port homodyne detection to realize super-resolution and super-sensitivity
• Ultimate phase estimation in a squeezed-state interferometer using photon counters with a finite number resolution