How Long Must a Phase Remember Itself? Coherence-Time Requirements for Controlled Transit

A controlled transit is a coherent process: the phase must mean the same thing at arrival as it did at departure. This paper derives the coherence-time requirement that follows from a transit's duration. With fidelity F = exp(-T_tr/T2), a sixty-second chamber transit retains fidelity 0.3679 if the coherence time is also sixty seconds, 0.9835 if coherence lasts an hour, and 0.9993 if it lasts a day. A design rule requiring one decade of margin sets the needed coherence time at ten times the transit duration: 0.01 s for a millisecond transit, 600 s for the chamber case, and 36000 s for an hour-long transit. The slow transits that the energy analysis favours are therefore exactly the transits that coherence finds hardest, and the two requirements must be optimised together rather than separately. Computed from stated assumptions; not measured. SIMULATED, NOT MEASURED.