Non-orthogonal positive operator valued measure phase distributions of one- and two-mode electromagnetic fields

摘要

Non-orthogonal positive operator valued measure (POVM) phase distributions are analysed for one-mode and two-mode electromagnetic (em) waves. For a one-mode ern field the non-orthogonal POVM phase distribution is given indirectly from the one-mode density matrix which is obtained by measurements of the quadrature probability distribution and a certain integration based on sampling pattern functions. The compensation for non-unitary detection is demonstrated by making explicit calculations for coherent states. For a two-mode em field the non-orthogonal POVM relative phase distribution is related to an angular momentum basis and two-mode angular momentum phase states. We compare our analysis with two-mode phase measurements made by other authors.We demonstrate the use of the present methods by analysing the phase distribution for the em field output from a Mach-Zehnder interferometer. For the case of coherent state input the phase distribution is obtained using the one-mode non-orthogonal POVM method, since in this case we get two coherent state outputs which are not correlated. For the case of a number state input the phase distribution is analysed by the two-mode non-orthogonal POVM method as there are strong correlations between the two em wave outputs.