Quantum polyspectra for modeling and evaluating simultaneous quantum measurements

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Quantum polyspectra have recently appeared as a new uncompromising approach to continuous quantum measurements. They allow for addressing an extremely broad class of experiments covering quantum-electronics, spin noise spectroscopy, and circuit quantum electrodynamics (cQED) making them the future swiss army knife of continuous quantum measurements. Polyspectra are the natural higher-order generalization of the well-known second-order spectra and can be directly calculated from the frequency resolved noisy detector output z(t) of an experiment. Analytic quantum polyspectra of a model master equation can be fitted to measured spectra for obtaining system parameters like coupling constants, tunneling rates, precessing frequencies, etc. In contrast to previous approaches like the n-resolved master equation (full counting statistics), the new approach works in the full regime between Gaussian-dominated noise and telegraph noise as found in spin noise measurements and quantum transport, respectively. We successfully applied quantum polyspectra to transport measurements on quantum dots in 2021. In this project, we will generalize the quantum-polyspectra framework to the important case of simultaneous measurements of two or more detectors with non-commuting measurement operators. Such experiments have recently become possible on superconducting qubits in the context of cQED. In particular (i) we will derive analytical expression for quantum polyspectra up to fourth order for up to four detectors; (ii) we will develop and provide a Python-based toolbox for the fast calculation of multivariate polyspectra from data empowering experimentalist to analyze their own data; (iii) we will provide a toolbox based on QuTiP for the calculation of analytic polyspectra from model Liouvillians (covering Hamiltonian dynamics, measurement back-action, environmental damping, temperature) (iv) We will apply our framework to urgent challenging questions about the non-Gaussian environmental noise in cQED and new multi-detector schemes in quantum transport. We expect a high impact of quantum polyspectra both on evaluating actual measurements and on the theoretical foundations of quantum-limited measurements.