Single biphoton ququarts as either pure or mixed states

Abstract

We analyze features of mixed biphoton polarization states, which arise from pure states of polarization-frequency biphoton ququarts after averaging over frequencies of photons. For mixed states, we find their concurrence $C$, Schmidt parameter $K$, degree of polarization $P$, as well as the von Neumann mutual information $I$. In some simple cases, we also find the relative entropy ${S}_{\mathrm{rel}}$ and the degree of classical correlations ${C}_{\mathrm{cl}}$. In mixed states, the Schmidt parameter does not characterize the degree of entanglement anymore, as it does in pure states. Nevertheless, the Schmidt parameter remains useful even in the case of mixed states because it remains directly related to the degree of polarization. We compare results occurring in the cases of full pure polarization-frequency states of ququarts and mixed states (averaged over frequencies). Differences between these results can be seen in experiments with and without frequency filters in front of a detector.