A three-stage adaptive method using locally informationally complete Fisher-symmetric measurements estimates pure states with O(d/N) error scaling and infidelity close to the Gill-Massar lower bound using 7d-3 outcomes.
Jozsa, Fidelity for Mixed Quantum States Journal of Modern Optics 41, 2315–2323 (1994)
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Near-optimal pure state estimation with adaptive Fisher-symmetric measurements
A three-stage adaptive method using locally informationally complete Fisher-symmetric measurements estimates pure states with O(d/N) error scaling and infidelity close to the Gill-Massar lower bound using 7d-3 outcomes.