Extended Data Fig. 1: Quantum projection noise in a dual-quadrature measurement.
From: Multi-ensemble metrology by programming local rotations with atom movements
a, Added standard deviation due to quantum projection noise (QPN) for phase estimation around different average phases \(\bar{\theta }\), plotted for N = 20 atoms utilized in a single-quadrature (orange) or dual-quadrature (green, 10 atoms per quadrature) measurement. The added QPN varies with the phase the measurement is taken at; thus as the prior width of the phase distribution grows over time, and a broader range of phases is sampled, the QPN will vary. b, To learn the prior width from the measured width we sample random phases from a normal distribution, followed by sampling the observed phase from a binomial random process representing the projection uncertainty (inset). We use the sampled distributions for the dual-quadrature estimator to calculate the width including QPN for a range of prior laser widths. We then invert this function and interpolate if needed, to find the prior width for any measured width.
