Determine the sampling method for information-gain optimization

Determine how random quantum states should be sampled when optimizing expected information gain for the Quantum Plumber’s Problem, so that the resulting strategy can reach the exact zero-probability conditions required to complete games.

Background

The paper considers a brute-force Monte Carlo strategy that samples candidate quantum input states and selects the state with the largest expected information gain. Uniform sampling over the projective Hilbert space performs well initially but fails to complete games because the states capable of ruling out blockage locations lie on measure-zero subspaces. The authors therefore identify the choice of sampling procedure as an unresolved issue relevant to constructing reliable game-completion strategies.

References

However, this still leaves open the question of how the random quantum states are sampled.

— The Quantum Plumber's Problem  (2609.11416 - Underwood et al., 10 Sep 2026) in Section 3.3, “Both Rulesets: A strategy of information gain maximisation”

At present, we are yet to pin down the mechanism for this suspected failure mode although we believe it could be due to an over-aversion to ``losing information''.

— The Quantum Plumber's Problem  (2609.11416 - Underwood et al., 10 Sep 2026) in Section 4.2, “Benefits of Losing Information”