Interferometric information gain versus interaction-free measurement - art. no. 052102

Interaction-free measurement schemes with ideal Mach-Zehnder interferometer s promised to distinguish absorptive samples with lower average absorption than simple transmission schemes. We show that this is only true for an ens emble 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 interm ediate transmission is introduced, but no phase shift is permitted, the cos t of information gain in terms of absorbed particles in the samples is high er in the interferometric scheme. We also investigate the general case of s amples with a continuous range of transmission and phase shift values, such that an interferometer's ability to measure both sample characteristics ca n be exploited. With an interferometer the number of principally distinguis hable samples increases linearly with the number of probe particles, but wi th a simple transmission setup it increases as the square root. When wishin g to distinguish twice as many samples from a continuous sample distributio n with an interferometric scheme, the number of absorbed particles per samp le only doubles, but it quadruples with a simple transmission scheme.