# Quantum Phase Sensitivity with Generalized Coherent States Based on Deformed su(1,1) and Heisenberg Algebras

## TL;DR

This paper explores how generalized coherent states based on deformed algebras can improve phase sensitivity in quantum interferometry, approaching fundamental quantum limits for enhanced sensing.

## Contribution

It introduces a new class of generalized coherent states from deformed algebras and analyzes their potential for surpassing classical phase measurement limits.

## Key findings

- Generalized coherent states enable near-quantum-limit phase sensitivities.
- Different detection methods are compared for optimal phase estimation.
- Parameter tuning enhances nonclassical features and measurement precision.

## Abstract

We investigate the phase sensitivity of a Mach-Zehnder interferometer using a special class of generalized coherent states constructed from generalized Heisenberg and deformed $su(1,1)$ algebras. These states, derived from a perturbed harmonic oscillator with a four parameter deformed spectrum, provide enhanced tunability and nonclassical features. The quantum Fisher information and its associated quantum Cramer-Rao bound are computed to define the fundamental precision limits in phase estimation. We analyze the phase sensitivity under three realistic detection methods: difference intensity detection, single mode intensity detection, and balanced homodyne detection. The performance of each method is compared with the quantum Cramer Rao bound to evaluate their optimality. Our results demonstrate that, for suitable parameter regimes, these generalized coherent states enable phase sensitivities approaching the quantum limit. This offers a flexible framework for precision quantum metrology and potential applications in quantum enhanced sensing.