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We show that when the speed of control is bounded, there is a widely applicable minimal-time control problem for which a coherent feedback protocol is optimal, and is faster than all measurement-based feedback protocols, where the latter are defined in a strict sense. The superiority of the coherent protocol is due to the fact that it can exploit a geodesic path in Hilbert space, a path that measurement-based protocols cannot follow.National Science Foundation (U.S.) (Project PHY-1005571)National Science Foundation (U.S.) (Project PHY-1212413)United States. Army Research Office. Multidisciplinary University Research Initiative (Grant W911NF-11-1-0268

Coherent feedback that beats all measurement-based feedback protocols