Polarization fluctuation as an entanglement monotone for entangled two-level systems

In a pure system consisting of a two-level atom (qubit) entangled with an arbitrary environment, the polarization fluctuation about the Schmidt axis is shown to preserve majorization. This polarization fluctuation is additive over independent two-level systems and is proposed to be an experimentally accessible entanglement monotone for a generic gas of two-level atoms entangled with a common bath.