Test of mutually unbiased bases for six-dimensional photonic quantum systems

TL;DR

This paper experimentally tests sets of three mutually unbiased bases in a six-dimensional photonic quantum system, providing insights into their structure and potential applications in quantum information processing.

Contribution

It demonstrates the implementation and testing of three MUBs in a six-dimensional photon system using a novel holographic technique, addressing a key open problem in quantum information theory.

Findings

Close agreement between experimental results and theoretical predictions

Successful implementation of MUBs in hybrid polarization-orbital angular momentum space

Potential applications in quantum state tomography and quantum key distribution

Abstract

In quantum information, complementarity of quantum mechanical observables plays a key role. If a system resides in an eigenstate of an observable, the probability distribution for the values of a complementary observable is flat. The eigenstates of these two observables form a pair of mutually unbiased bases (MUBs). More generally, a set of MUBs consists of bases that are all pairwise unbiased. Except for specific dimensions of the Hilbert space, the maximal sets of MUBs are unknown in general. Even for a dimension as low as six, the identification of a maximal set of MUBs remains an open problem, although there is strong numerical evidence that no more than three simultaneous MUBs do exist. Here, by exploiting a newly developed holographic technique, we implement and test different sets of three MUBs for a single photon six-dimensional quantum state (a qusix), encoded either in a hybrid polarization-orbital angular momentum or a pure orbital angular momentum Hilbert space. A close agreement is observed between theory and experiments. Our results can find applications in state tomography, quantitative wave-particle duality, quantum key distribution and tests on complementarity and logical indeterminacy.