  There has been an intense debate on the quantum versus classical origin of
ghost imaging with a thermal light source over the last two decades. A lot of
distinguished work has contributed to this topic, both theoretically and
experimentally, however, to this day this quantum-classical dilemma still
persists. Here we formulate for the first time a density matrix in the photon
orbital angular momentum (OAM) Hilbert space to fully characterize the two-arm
ghost imaging system with the basic definition of thermal light sources. Our
formulation offers a mathematically precise method to describe the formation of
a ghost image in a nonlocal fashion. More importantly, it provides a more
physically intuitive picture to reveal the quantumness hidden in the thermal
ghost imaging, and therefore, presenting a sound resolution to the ongoing
quantum-classical dilemma, which distinguishes the quantum correlations beyond
entanglement in terms of geometric measure of discord. Our work also suggests
further studies of using thermal multi-photon OAM states directly to implement
some quantum information tasks.
