Probability distributions for the phase difference

Abstract

In this work we analyze the quantum phase properties of pairs of electromagnetic field modes. Since phases differing by 2π are physically indistinguishable, we propose a general procedure to obtain the correct mod(2π) probability distributions for the phase difference. This allows us to investigate the properties of a number of phase approaches. This procedure provides deeper insight into the quantum nature of the phase difference. We relate this problem to the representation of nonbijective canonical transformations in quantum mechanics.