📝 SummarXiv

Abstract

I present a concise, first principles metrological framework for imaging dielectric biomaterials by probing the full phase space (Wigner) distribution of a quantum electromagnetic field. Building on a rigorous multilayer Maxwell and Cole Cole model for stratified tissue, my method (Quantum Phase space Tomography, QPST) couples analytical forward theory with quantum metrology and Bayesian inference. I prepare a structured quantum EM probe (e.g. a squeezed microwave pulse) that interacts with tissue and then perform full quantum state tomography of the outgoing field. The recovered Wigner quasi probability reveals subwavelength and non classical features lost in classical imaging. By projecting the measurement onto the analytically derived tissue response manifold, I recover key physiological parameters (e.g. layer thickness, dispersion). I further define a Dielectric Anaplasia Metric (DAM) that quantifies tissue microstructural heterogeneity (e.g. malignancy) via deviations in Cole Cole parameters. My design leverages state of the art quantum sensors (e.g. NV diamond magnetometers) and advanced inverse algorithms (physics informed neural networks, diffusion priors). Numerical examples demonstrate that QPST can non invasively map tissue permittivity with unprecedented sensitivity. This work bridges fundamental electromagnetic theory and emerging quantum technologies, promising a new paradigm for medical imaging.