Tomography from collective measurements

TL;DR

This paper presents a method for quantum state tomography of N-qubit states using collective measurements, focusing on symmetric states and decomposing non-symmetric states into SU(2) blocks, with a simplified reconstruction protocol for symmetric sectors.

Contribution

It introduces an exact tomography method for symmetric N-qubit states and a decomposition approach for non-symmetric states into SU(2) blocks, simplifying the reconstruction process.

Findings

Exact tomography for symmetric states

Decomposition of non-symmetric states into SU(2) blocks

Simplified reconstruction protocol for symmetric sector

Abstract

We discuss the tomography of $N$-qubit states using collective measurements. The method is exact for symmetric states, whereas for not completely symmetric states the information accessible can be arranged as a mixture of irreducible SU(2) blocks. For the fully symmetric sector, the reconstruction protocol can be reduced to projections onto a canonically chosen set of pure states.