Optimal quantum tomography of permutationally invariant qubits

TL;DR

This paper derives minimal measurement sets of mutually unbiased bases for efficient quantum state tomography of permutationally invariant multiqubit states, reducing measurement complexity by leveraging prior symmetry information.

Contribution

It introduces the first explicit construction of minimal mutually unbiased bases tailored for permutationally invariant multiqubit states.

Findings

Reduced the number of measurement bases needed for tomography

Provided explicit construction methods for these bases

Enhanced efficiency of quantum state reconstruction

Abstract

Mutually unbiased bases determine an optimal set of measurements to extract complete information about the quantum state of a system. However, quite often a priori information about the state exist, making some of the measurement bases superfluous. This is, for example, the case when multiqubit states belong to the permutationally invariant subspace. In this paper we derive the minimal sets of mutually unbiased bases needed to tomographically reconstruct such states.