Below is a more technical restatement and synthesis of the delayed-choice quantum eraser experiment, focusing on standard quantum-mechanical concepts such as the joint Hilbert space, measurement operators, partial traces, and conditional probabilities. It reiterates how the paradox of “seemingly retroactive choice” naturally arises from the entangled wavefunction and the way measurements are defined and correlated—without requiring backward causation.
- Hilbert Spaces:
- Let (\mathcal{H}_\text{signal}) be the Hilbert space describing the signal photon’s degrees of freedom (e.g., path through slit (A) vs. slit (B), transverse momentum, polarization, etc.).
- Let (\mathcal{H}_\text{idler}) be the Hilbert space describing the idler photon’s degrees of freedom.