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arXiv · 1304.4081

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

Vincenzo D'Ambrosio·Filippo Cardano·Ebrahim Karimi·Eleonora Nagali·Enrico Santamato·Lorenzo Marrucci·Fabio Sciarrino
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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.

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Vincenzo D'Ambrosio, Filippo Cardano, Ebrahim Karimi, Eleonora Nagali, Enrico Santamato, Lorenzo Marrucci, Fabio Sciarrino. 2013-04-15. Test of mutually unbiased bases for six-dimensional photonic quantum systems. https://doi.org/10.1038/srep02726

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