Quantum limits of exoplanet discovery around resolved stars

We investigate the quantum limits of exoplanet detection and localization around partially resolved stars with finite angular extent. In this model, the density operator describing the state of the incoming optical field has an infinite-dimensional support over the Hilbert space of band-limited square-normalized spatial modes. Therefore, we numerically evaluate two fundamental quantum bounds: (1) The quantum Chernoff exponent which provides an asymptotic lower bound on the minimum achievable probability of error for exoplanet detection, (2) The quantum Cramer-Rao bound which provides a lower bound on the minimum achievable uncertainty for unbiased estimators of the exoplanet orbital position. We subsequently compare the performance of even-order coronagraphs against these bounds and propose a new quantum-optimal coronagraph which can accelerate the rate of exoplanet discovery over the domain of sub-diffraction orbits.