Experimental proposal for symmetric minimal two-qubit state tomography

TL;DR

This paper proposes an experimental setup using linear optics to realize symmetric informationally complete measurements in a two-qubit system encoded in a single photon, advancing quantum state tomography techniques.

Contribution

It introduces a novel two-step approach to implement SIC POMs in a four-dimensional Hilbert space using linear optics.

Findings

Successful implementation of SIC POM with linear optics

New two-step measurement process demonstrated

Potential link between SIC POMs and mutually unbiased bases

Abstract

We propose an experiment that realizes a symmetric informationally complete (SIC) probability-operator measurement (POM) in the four-dimensional Hilbert space of a qubit pair. The qubit pair is carried by a single photon as a polarization qubit and a path qubit. The implementation of the SIC POM is accomplished with the means of linear optics. The experimental scheme exploits a new approach to SIC POMs that uses a two-step process: a measurement with full-rank outcomes, followed by a projective measurement on a basis that is chosen in accordance with the result of the first measurement. The basis of the first measurement and the four bases of the second measurements are pairwise unbiased --- a hint at a possibly profound link between SIC POMs and mutually unbiased bases.