Coherence, entanglement, and complementarity in mixed classical light

The classical analogues of quantum correlations have been the subject of considerable interest in the past few years; however, all of these investigations consider the classical analogue of only pure quantum mechanical states. In this work, we study mixed classical light states and derive relations between the polarization coherence of the field and the (classical) entanglement between its degrees of freedom. We show, for a specific model of mixed states, where the purity is determined by a single parameter, how the coherence shared between polarization and entanglement shrinks as the level of purity decreases. The sum of the square of polarization and entanglement remains constant, a behavior consistent with previous results [Phys. Rev. Lett.117, 153901 (2016)PRLTAO0031-900710.1103/PhysRevLett.117.153901] of pure states, even though the constant for the mixed-state case is now smaller in value.