Constraints between concurrence and polarization for mixed states subjected to open system dynamics

Entanglement and polarization are mutually constrained by the relationship C2+P2=1, which engages the concurrence C of a pure, two-qubit state and the degree of polarization P of either of its two subsystems. How the above constraint generalizes for mixed states is an open question. We address mixed, two-qubit states of the X type, i.e., those whose density matrix has nonzero elements only in the two main diagonals. We focus on mixed states that arise out of a pure, two-qubit state that is subjected to either the amplitude damping channel or the depolarizing channel. We derive alternative constraints for concurrence and polarization and test them experimentally with polarization-entangled photons. We argue that our theoretical results hold also for classical light, whenever two binary degrees of freedom can be entangled.