  The best performance of a Mach-Zehnder interferometer is achieved with the
input state |N_T/2 + 1>|N_T/2-1 > + |N_T/2 - 1>|N_T/2+1>, being N_T the total
number of atoms/photons. This gives: i) a phase-shift error confidence
C_{68%}=2.67/N_T with ii) a single interferometric measurement. Different input
quantum states can achieve the Heisenberg scaling ~ 1/N_T but with higher
prefactors and at the price of a statistical analysis of two or more
independent measurements.
