Paradox with Phase-Coupled Interferometers

Understand

A pair of interferometers can be coupled by allowing one path from each to overlap such that if the particles meet in this overlap region, they annihilate.

• It was shown by one of us over thirty years ago that such annihilation-coupled interferometers can exhibit apparently paradoxical behaviour.
• More recently, Bose et al.
• and Marletto and Vedral have considered a pair of interferometers that are phase-coupled (where the coupling is through gravitational interaction).