Pure-state tomography with parallel unentangled measurements

Quantum state tomography (QST) aims at estimating a quantum from averaged measurements made on copies of that state. Most algorithms rely QST some point and it is well-explored topic in the literature, mostly for mixed states. In this paper we focus pure using parallel unentangled measurements. Pure states are small but useful subset all states, their requires fewer essentially phase recovery problem. Parallel easy to implement practice because they allow user measure each qubit individually, e.g., one-qubit Pauli We propose two sets one can make as well use measurement outcomes order identify also discuss how those estimates be fine tuned by finding maximizes likelihood with different variants likelihood. The performances proposed three types methods validated means detailed numerical tests, including close being pure.