  Four types of photon counters are discussed in terms of information,
fidelity, and physical reversibility: conventional photon counter, quantum
counter, and their quantum nondemolition (QND) versions. It is shown that when
a photon field to be measured is in an arbitrary superposition of vacuum and
one-photon states, the quantum counter is the most reversible, the QND version
of conventional photon counter provides the most information, and the QND
version of quantum counter causes the smallest state change. Our results
suggest that the physical reversibility of a counter tends to decrease the
amount of information obtained by the counter.
