Squeezed vacuum as a universal quantum probe

TL;DR

This paper demonstrates that single- and two-mode squeezed vacuum states are optimal universal probes for quantum estimation of bilinear Hamiltonians, achieving the Heisenberg limit with feasible measurement strategies.

Contribution

It establishes the optimality of squeezed vacuum states for quantum parameter estimation and provides practical measurement schemes to approach the ultimate quantum limits.

Findings

Squeezed vacuum states achieve the Heisenberg limit in quantum estimation.

Homodyne detection with Bayesian analysis can nearly reach optimal sensitivity.

Gaussian states are effective resources for quantum metrology with current technology.

Abstract

We address local quantum estimation of bilinear Hamiltonians probed by Gaussian states. We evaluate the relevant quantum Fisher information (QFI) and derive the ultimate bound on precision. Upon maximizing the QFI we found that single- and two-mode squeezed vacuum represent an optimal and universal class of probe states, achieving the so-called Heisenberg limit to precision in terms of the overall energy of the probe. We explicitly obtain the optimal observable based on the symmetric logarithmic derivative and also found that homodyne detection assisted by Bayesian analysis may achieve estimation of squeezing with near-optimal sensitivity in any working regime. Besides, by comparison of our results with those coming from global optimization of the measurement we found that Gaussian states are effective resources, which allow to achieve the ultimate bound on precision imposed by quantum mechanics using measurement schemes feasible with current technology.