Temporally Localized Quantum Operations on Continuous-Wave Thermal Light

Previous work showed that thermal light with a blackbody spectrum cannot be decomposed into a mixture of independent localized pulses. However, we find that in the weak-source limit and under the assumption of a flat spectrum, the first nonvacuum term in the state expansion does form a mixture of such pulses. This decomposition is essential for quantum-enhanced astronomical interferometry, which typically operates on localized pulses even though stellar light is inherently continuous-wave. We present a quantum derivation of the van Cittert-Zernike theorem that incorporates finite bandwidth, thereby justifying the operations on localized pulses while processing continuous-wave thermal light. For general spectra in the weak-source limit, we establish a criterion under which correlations between pulses can be safely neglected. When this criterion is not met, we provide a corrected strategy that accurately accounts for both the spectral profile and the detector-defined pulse shape.