Determine when input-port-restricted games are completable

Determine whether the Quantum Plumber’s Problem can be completed for interferometers other than Hofmann’s three-path interferometer when the player is restricted to input-port states rather than arbitrary superpositions of the input ports.

Background

The paper considers a semi-quantum variant in which the player may prepare only the input-port states. For Hofmann’s interferometer, this restriction prevents the player from ruling out the blockage locations corresponding to P1, F, and P2, so the game cannot be completed. The authors leave unresolved whether other interferometer configurations might permit completion under the same input-port restriction.