  Quantum discord, a kind of quantum correlation, is defined as the difference
between quantum mutual information and classical correlation in a bipartite
system. In general, this correlation is different from entanglement, and
quantum discord may be nonzero even for certain separable states. Even in the
simple case of bipartite quantum systems, this different kind of quantum
correlation has interesting and significant applications in quantum information
processing. So far, quantum discord has been calculated explicitly only for a
rather limited set of two-qubit quantum states and expressions for more general
quantum states are not known. In this paper, we derive explicit expressions for
quantum discord for a larger class of two-qubit states, namely, a
seven-parameter family of so called X-states that have been of interest in a
variety of contexts in the field. We also study the relation between quantum
discord, classical correlation, and entanglement for a number of two-qubit
states to demonstrate that they are independent measures of correlation with no
simple relative ordering between them.
