Simultaneous estimation of relative phase and coherence in astronomical interferometry

Astronomical interferometry relies on measuring the complex degree of coherence—comprising both a modulus and a relative phase—to reconstruct the spatial intensity distribution of distant sources. While previous research has often treated these parameters in isolation, this paper investigates the simultaneous estimation of both parameters to provide a more realistic assessment of imaging performance. Specifically, it compares the fundamental precision limits of direct interferometry against continuous-variable (CV) quantum teleportation schemes.

The authors employ the framework of multiparameter quantum estimation theory. They calculate the Quantum Cramér-Rao Bound (QCRB) for both schemes, which sets the ultimate limit on estimation precision. Despite the non-commutativity of the symmetric logarithmic derivative operators associated with the phase and coherence, the authors demonstrate that the mean Uhlmann curvature matrix is zero, ensuring that the QCRB remains an asymptotically tight bound. They further evaluate the performance of Gaussian measurements, specifically identifying the conditions under which heterodyne detection approaches optimality.

The study reveals that direct interferometry consistently yields a lower QCRB than the CV quantum teleportation scheme, indicating superior precision in the lossless regime. While both schemes see improved performance as the mean photon number increases, the direct scheme remains the more precise option under standard conditions. However, the authors find that the relative performance is sensitive to transmission loss: direct interferometry is superior for short baselines, whereas CV quantum teleportation becomes more effective as the baseline length increases and transmission losses become more severe.

This work clarifies the trade-offs between classical-like direct detection and quantum-enhanced teleportation in astronomical imaging. By framing the problem as a simultaneous estimation task, the authors provide a more rigorous benchmark for evaluating whether quantum resources actually offer a practical advantage in real-world observational scenarios. The identification of heterodyne detection as a near-optimal measurement strategy in the high-photon-number regime offers a clear path for implementing these theoretical insights in current astronomical arrays.