Abstract
Quantum-enhanced, idler-free sensing protocol to measure the response of a
target object to the frequency of a probe in a noisy and lossy scenario is
proposed. In this protocol, a target with frequency-dependent reflectivity 𝜼�(𝝎�)
embedded in a thermal bath is considered. The aim is to estimate the
parameter 𝝀� = 𝜼�(𝝎�2 ) − 𝜼�(𝝎�1 ), since it contains relevant information for
different problems. For this, a bi-frequency quantum state is employed as the
resource, since it is necessary to capture the relevant information about the
parameter. Computing the quantum Fisher information H relative to the
parameter 𝝀� in an assumed neighborhood of 𝝀� ≈ 0 for a two-mode squeezed
state (HQ ), and a pair of coherent states (HC ), a quantum enhancement is
shown in the estimation of 𝝀�. This quantum enhancement grows with the
mean reflectivity of the probed object, and is noise-resilient. Explicit formulas
are derived for the optimal observables, and an experimental scheme based
on elementary quantum optical transformations is proposed. Furthermore,
this work opens the way to applications in both radar and medical imaging, in
particular in the microwave domain.