Realizing quantum advantage without entanglement in single-photon states

Quantum discord expresses quantum correlations beyond those associated with entanglement.\footnote{K Modi, {\em et al., Rev. Mod. Phys. } \bf{84}, 1655 (2012)}. Although it has been extensively studied theoretically, quantum discord has yet to become a standard tool in experimental studies of correlation. We propose a class of experiments in which quantum correlations are present in the absence of entanglement, and are best understood in terms of quantum discord.. These utilize X-states of two qubits, which correspond to the polarization and the optical path of a single photon within a Mach-Zehnder interferometer. We show how to produce states with diverse measures of discord and entanglement, including the case of discord without entanglement. With these states we show how a classical random variable $K$ can be encoded by Alice and decoded by Bob. Using our previous results \footnote{A. Maldonado-Trapp, {\em et al., Quantum Inf. Process} \bf{14} 1947 (2015)} we analytically study the correlations between the spin and path qubits and its relation with the information about $K$ that can be decoded by Bob using local measurements with or without two-qubit gate operations.\footnote{M. Gu, {\em et al., Nature Phys. }\bf{8}, 671 (2012)}