Quantum Detectability in Invisibility Cloaks
Classical invisibility cloaks are designed to suppress selected scattering signatures and thereby make an object appear absent to external electromagnetic probes. However, the suppression of a classical scattering observable does not, by itself, establish that all information about the concealed object has been removed from the detected quantum state of light. Here we formulate the detectability of classically cloaked objects as a quantum-state distinguishability problem. Treating a linear passive cloak as an effective Gaussian quantum channel acting on the accessible detected modes, we show that local quantum undetectability requires the detected first and second moments to be independent of the hidden-object parameter. In this framework, quantum Fisher information provides an operational criterion for whether the concealed parameter remains estimable from the detected output state. We derive displacement- and covariance-level detectability conditions and show that a nonzero parameter imprint surviving in the detected Gaussian state leads to a nonzero accessible quantum Fisher information. To connect the criterion with a physical cloaking model, we analyze a regularized cylindrical transformation-optical cloak in the Born limit and compare the scaling of the classical scattering response with the derivative-based quantum sensitivity. The analysis shows that reducing a scattering amplitude is not equivalent to eliminating local quantum-state sensitivity. Loss, environmental noise, and finite numerical aperture degrade the accessible information, but quantum undetectability is reached only when the parameter imprint is removed from the detected state or projected entirely outside the accessible subspace. These results provide a Gaussian-channel framework for assessing when classical cloaking does, and does not, imply quantum-state undetectability.