  The superposition of quantum states lies at the heart of physics and has been
recently found to serve as a versatile resource for quantum information
protocols, defining the notion of quantum coherence. In this contribution, we
report on the implementation of its complementary concept, coherence from
quantum measurements. By devising an accessible criterion which holds true in
any classical statistical theory, we demonstrate that noncommutative quantum
measurements violate this constraint, rendering it possible to perform an
operational assessment of the measurement-based quantum coherence. In
particular, we verify that polarization measurements of a single photonic
qubit, an essential carrier of one unit of quantum information, are already
incompatible with classical, i.e., incoherent, models of a measurement
apparatus. Thus, we realize a method that enables us to quantitatively certify
which quantum measurements follow fundamentally different statistical laws than
expected from classical theories and, at the same time, quantify their
usefulness within the modern framework of resources for quantum information
technology.
