Continuous-variable quantum probes for structured environments

TL;DR

This paper explores the use of continuous-variable quantum probes, specifically Gaussian states of bosonic modes, to estimate parameters of structured environments like Ohmic reservoirs, achieving optimal precision limits with feasible measurements.

Contribution

It introduces a method using Gaussian states for quantum parameter estimation in structured environments and identifies conditions for optimal measurement and probe tuning.

Findings

Homodyne detection achieves quantum-limited precision.

Optimal probe conditions depend on initial state, temperature, and interaction time.

Invariant sweet spots enable optimal estimation regimes.

Abstract

We address parameter estimation for complex/structured systems and suggest an effective estimation scheme based on continuous-variables quantum probes. In particular, we investigate the use of a single bosonic mode as a probe for Ohmic reservoirs, and obtain the ultimate quantum limits to the precise estimation of their cutoff frequency. We assume the probe prepared in a Gaussian state and determine the optimal working regime, i.e. the conditions for the maximization of the quantum Fisher information in terms of the initial preparation, the reservoir temperature and the interaction time. Upon investigating the Fisher information of feasible measurements we arrive at a remarkable simple result: homodyne detection of canonical variables allows one to achieve the ultimate quantum limit to precision under suitable, mild, conditions. Finally, upon exploiting a perturbative approach, we find the invariant sweet spots of the (tunable) characteristic frequency of the probe, able to drive the probe towards the optimal working regime.