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

We experimentally verify the uncertainty relations for the mixed states in tomographic representation by measuring the radiation field tomograms, i.e. homodyne distributions. Thermal states of a single-mode radiation field are discussed in detail as a paradigm of the mixed quantum state. On considering the connection between generalized uncertainty relations and optical tomograms, it is seen that the purity of the states can be retrieved by statistical analysis of the homodyne data. The purity parameter assumes a relevant role in quantum information where the effective fidelities of protocols depend critically on the purity of the information carrier states. In this context, the homodyne detector becomes an easy-to-handle purity-meter for the state on line with a running quantum information protocol.