Beating noise in frequency estimation with squeezing and memory in continuous-variable systems

TL;DR

This paper explores how Hamiltonian engineering and non-Markovian environmental effects can improve frequency estimation precision in noisy continuous-variable quantum systems, surpassing classical limits.

Contribution

It introduces methods to enhance quantum Fisher information through structured Hamiltonians and non-Markovian dynamics, demonstrating potential for robust quantum metrology.

Findings

Embedding squeezing into the Hamiltonian increases sensitivity at short times.

Structured environments with memory induce information backflow, improving estimation.

Gaussian measurements can saturate the quantum Fisher information under certain regimes.

Abstract

Quantum metrology promises precision beyond classical limits, yet environmental noise typically degrades the quantum resources required for such enhancement. In this work, we investigate frequency estimation in noisy continuous-variable systems, focusing on two complementary strategies to mitigate decoherence: Hamiltonian engineering and the exploitation of non-Markovian dynamics. By embedding squeezing directly into the system Hamiltonian, we show that the quantum Fisher information (QFI) may acquire a tunable higher-order time dependence, leading to enhanced sensitivity in the short-time regime. Moving beyond the Markovian approximation, we employ the quantum Brownian motion model to demonstrate that structured environments with finite memory can induce information backflow, temporarily restoring and even improving estimation precision relative to the unitary limit. We further assess the achievability of these bounds via Gaussian measurements, identifying regimes where homodyne, heterodyne, and optimized general-dyne measurements saturate the QFI, and noting that stronger squeezing widens the gap, potentially requiring non-Gaussian measurement strategies. Our results establish that jointly tailoring system Hamiltonian and environmental memory offers a viable route toward robust quantum-enhanced frequency estimation in open systems.