Quantum Erasure Imaging: Complementary Modalities from Delayed-Choice Erasure

Quantum Erasure Imaging (QEI) turns delayed-choice erasure into a practical imaging protocol. Entangled photon pairs encode two classical modalities, absorption $T(x,y)$ and a phase-sensitive cosine quadrature of $\phi(x,y)$, reconstructed from a single run of time-tagged coincidences by retrospective sorting on a remote ancilla. Measuring the ancilla in H/V yields $T$ via which-path information; D/A yields interference visibility $\propto \frac{2\sqrt{T}}{T+1}\cos\phi$; and a rotated orthonormal analyzer continuously trades between them. We derive balanced two-port estimators whose denominators are analyzer independent (completeness / no signaling), together with Fisher information (FI) and Cram\'er--Rao bounds (CRBs) that establish an equivalence to time division under labeled randomization. The advantages of QEI are operational: single-run acquisition, perfect co-registration, and remote / delayed mode choice. We illustrate the protocol with Monte-Carlo simulations and open source our code.