Bars are one minus the ratio of the Holevo bound to the m -copy Nagaoka bound, for m up to and including 7, calculated theoretically at ϵ = 0.5. Experimental points are one minus the ratio of the Holevo bound to the m.s.e. obtained experimentally. Unfilled black diamonds correspond to the precision that our three- and four-copy projective measurements can obtain in theory. The upper and lower filled black diamonds are simulations based on a depolarizing noise model with gate error rates of 5 × 10 −3 and 1 × 10 −3, respectively. The legend is the same as in e. In all figures the dashed pink, purple and green lines correspond to the single-copy Nagaoka, two-copy Nagaoka and Holevo bounds, respectively. The orange-shaded region corresponds to the m.s.e. attainable with separable measurements. m.s.e.s below the dashed green line are forbidden by quantum mechanics. Error bars are obtained using the bootstrapping technique 52 and correspond to one standard deviation. All experimental points have error bars but some are smaller than the marker size. Each data point corresponds to the average of 400 individual experimental runs, each using 512 shots, as shown in the inset of a (see Methods for details).
