  The interaction of a quantum system with the environment leads to the
so-called quantum decoherence. Beyond its fundamental significance, the
understanding and the possible control of this dynamics in various scenarios is
a key element for mastering quantum information processing. Here we report the
quantitative probing of what can be called the quantum decoherence of
detectors, a process reminiscent of the decoherence of quantum states in the
presence of coupling with a reservoir. We demonstrate how the quantum features
of two single-photon counters vanish under the influence of a noisy
environment. We thereby experimentally witness the transition between the
full-quantum operation of the measurement device to the "semi-classical
regime", described by a positive Wigner function. The exact border between
these two regimes is explicitely determined and measured experimentally.
