Violations of Bell’s Inequality in an eight-port receiver

Abstract

It is shown that a system of correlated electromagnetic field modes in an eight-port balanced homodyne detector is useful for testing Bell's inequality. This system is different from all previously considered tests of Einstein locality that use photons1-3 in that the correlated field modes present in the eight-port are all of the same polarization, and no polarizing filters are used. The variables that replace the angular orientation of the polarizing filters in the other systems are the optical path lengths between the beam splitters in the eight-port. A variety of different states of the free electromagnetic field may be tested for violations of locality using this system. It is shown that combinations of a number state and any other free- field state as inputs to the eight-port can demonstrate violations of the inequality, thus indicating the failure of locality for a specific set of input states.