Single-qubit Pauli measurement tomography for sparse pure states

Determine whether there exists an algorithm for learning n-qubit k-sparse pure states to infidelity at most ε in approximately O(kn/ε) time using only single-qubit Pauli measurements.

Background

The paper's pure-state algorithm achieves near-optimal time complexity using low-depth CNOT circuits followed by single-qubit Pauli measurements. It leaves unresolved whether the same runtime can be achieved under the stricter measurement model in which only single-qubit Pauli measurements are permitted, without the additional two-qubit operations used by the proposed approach.