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Optimal Pure-State Qubit Tomography via Sequential Weak Measurements
October 17, 2018
A sequence of weak isotropic measurements can yield the optimal measurement of a collection of identical qubits — a POVM over the continuous set of spin-coherent states. We show here a numerical simulation for an independent sequence of collective isotropic weak measurements on an ensemble of 50 qubits. The vertical axis is a measure how close a POVM element is to a spin-coherent state projector with the value the “coherency” C=1 corresponding to a spin-coherent state. The olive region consists of the coherency for 50 samples of the measurement record as a function of time. The spheres are Husimi distributions of the POVM element (left) and the post-measurement state (right) for various times of the black sample trajectory. The POVM converges asymptotically, extracting the estimated direction of the unknown spin, whilst the state does not change drastically, because the measurements are weak.