  Quantum systems in mixed states can be unentangled and yet still correlated
in a way that is not possible for classical systems. These correlations can be
quantified by the quantum discord and might provide a resource for certain
mixed-state quantum information processing tasks. Here we report on the
generation of discordant states of two trapped atomic ions via Markovian
decoherence processes. While entanglement is strictly non-increasing under such
operations, discord can be generated in various forms. Firstly we show that,
starting from two classically correlated qubits, it is possible to generate
discord by applying decoherence to just one of them. Secondly, even when
starting with completely uncorrelated systems, we show that discord can be
generated via classically correlated decoherence processes. Finally, the Werner
states are created. The generated states can be used as a resource state for
quantum information transmission and could be readily extended to more ions.
