Optimal Pure-State Qubit Tomography via Sequential Weak Measurements

TL;DR

This paper demonstrates that optimal pure-state qubit tomography can be achieved through a sequence of weak, collective measurements of spin projections, approaching theoretical bounds with numerical evidence.

Contribution

It introduces a method to realize the spin-coherent-state POVM via sequential weak measurements, advancing quantum tomography techniques.

Findings

Sequential weak measurements approach optimal bounds

Numerical simulations confirm effectiveness

Method applicable to pure qubit state tomography

Abstract

The spin-coherent-state positive-operator-valued-measure (POVM) is a fundamental measurement in quantum science, with applications including tomography, metrology, teleportation, benchmarking, and measurement of Husimi phase space probabilities. We prove that this POVM is achieved by collectively measuring the spin projection of an ensemble of qubits weakly and isotropically. We apply this in the context of optimal tomography of pure qubits. We show numerically that through a sequence of weak measurements of random directions of the collective spin component, sampled discretely or in a continuous measurement with random controls, one can approach the optimal bound.