Preparation information and optimal decompositions for mixed quantum states

Consider a joint quantum state of a system and its environment. A measureme nt on the environment induces a decomposition of the system state. Using al gorithmic information theory, we der ne the preparation information of a pu re or mixed state in a given decomposition. We then der ne an optimal decom position as a decomposition for which the average preparation information i s minimal. The average preparation information for an optimal decomposition characterizes the system-environment correlations. We discuss properties a nd applications of the concepts introduced above and give several examples.