Probing light polarization with the quantum Chernoff bound
Iulia Ghiu, Gunnar G. Bjork, Paulina Marian, Tudor A. Marian · Physical Review A · 2010
We recall the framework of a consistent quantum description of polarization of light. Accordingly, the degree of polarization of a two-mode state $\mathrm{\ensuremath{\rho}\ifmmode \hat{}\else \^{}\fi{}}$ of the quantum radiation field can be defined as a distance of a related state ${\mathrm{\ensuremath{\rho}\ifmmode \hat{}\else \^{}\fi{}}}_{b}$ to the convex set of all SU(2)-invariant two-mode states. We explore a distance-type polarization measure in terms of the quantum Chernoff bound and derive its explicit expression. A comparison between the Chernoff and Bures degrees of polarization leads to interesting conclusions for some particular states chosen as illustrative examples.