Multilevel Quantum Coherence

Quantum coherence is one of the fundamental features that mark the departure of quantum mechanics from the classical realm. It manifests whenever a system exists in a superposition of classically distinguishable states, and for many-body systems embodies the essence of entanglement. For gauging the nonclassicality of a system, however, it is important to go beyond the mere presence or absence of coherence. Just like in the case of entanglement, there is a rich structure of multilevel coherence, which might be interesting for applications in quantum information processing and beyond. Using four-dimensional photonic quantum systems, I will show how a number of ways to experimentally quantify the coherence present in a quantum system. In particular, multilevel coherence is found to be the fundamental resource for an elementary quantum information task, which in turn can be exploited to witness the presence of coherence even without knowing what your measurement device is doing.