Homodyne estimation of quantum state purity by exploiting the covariant uncertainty relation

Abstract

We experimentally verify uncertainty relations for mixed states in the\ntomographic representation by measuring the radiation field tomograms, i.e.\nhomodyne distributions. Thermal states of single-mode radiation field are\ndiscussed in details as paradigm of mixed quantum state. By considering the\nconnection between generalised uncertainty relations and optical tomograms is\nseen that the purity of the states can be retrieved by statistical analysis of\nthe homodyne data. The purity parameter assumes a relevant role in quantum\ninformation where the effective fidelities of protocols depend critically on\nthe purity of the information carrier states. In this contest the homodyne\ndetector becomes an easy to handle purity-meter for the state on-line with a\nrunning quantum information protocol.\n