Generic Two-Mode Gaussian States as Quantum Sensors

TL;DR

This paper explores how two-mode Gaussian states can be used as quantum sensors to precisely estimate parameters of Gaussian channels, such as beam splitter transmissivity and squeezing, with implications for quantum metrology.

Contribution

It introduces a framework leveraging quantum Fisher information to analyze the metrological usefulness of two-mode Gaussian states for parameter estimation.

Findings

Symmetry in mode mixing enhances quantum Fisher information.

Transmissivity significantly affects estimation precision.

Two-mode Gaussian states are effective for quantum thermometry.

Abstract

Gaussian quantum channels constitute a cornerstone of continuous-variable quantum information science, underpinning a wide array of protocols in quantum optics and quantum metrology. While the action of such channels on arbitrary states is well-characterized under full channel knowledge, we address the inverse problem, namely, the precise estimation of fundamental channel parameters, including the beam splitter transmissivity and the two-mode squeezing amplitude. Employing the quantum Fisher information (QFI) as a benchmark for metrological sensitivity, we demonstrate that the symmetry inherent in mode mixing critically governs the amplification of QFI, thereby enabling high-precision parameter estimation. In addition, we investigate quantum thermometry by estimating the average photon number of thermal states, revealing that the transmissivity parameter significantly modulates estimation precision. Our results underscore the metrological utility of two-mode Gaussian states and establish a robust framework for parameter inference in noisy and dynamically evolving quantum systems.