Abstract:
Interaction-free measurement schemes with ideal Mach-Zehnder interferometers promised to distinguish absorptive samples with lower average
absorption than simple transmission schemes. We show that this is only
true for an ensemble of two kinds of samples, where one kind is highly
absorptive and the other is highly transmissive. As soon as a third kind of
sample with intermediate transmission is introduced, but no phase shift
is permitted, the cost of information gain in terms of absorbed particles
in the samples is higher in the interferometric scheme. We also investigate the general case of samples with a continuous range of transmission
and phase shift values, such that an interferometer's ability to measure
both sample characteristics can be exploited. With an interferometer the
number of principally distinguishable samples increases linearly with the
number of probe particles, but with a simple transmission setup it in-
creases as the square root. When wishing to distinguish twice as many
samples from a continuous sample distribution with an interferometric
scheme, the number of absorbed particles per sample only doubles, but it
quadruples with a simple transmission scheme.