Determine whether repeated edges reduce quantum space for Noisy Gap Cycle

Determine whether allowing repeated edges in uniformly random-order Noisy Gap Cycle streams permits a quantum streaming algorithm using less space than the Ω(n) lower bound proved for single-arrival streams.

Background

The paper proves an Ω(n) one-pass quantum space lower bound for Noisy Gap Cycle when every edge appears exactly once and the edges arrive in uniformly random order. The proof relies on a robust communication reduction in which a random partition of stream items gives the two parties complementary information.

With repeated edges, copies of the same edge may be exposed to both parties, changing the communication structure and potentially enabling replenishment-like strategies. The paper therefore leaves open whether repetition can lower the required quantum space.