Correlation between Correlations: Process and Time in Quantum Networks
  We study a special inhomogeneous quantum network consisting of a ring of $M$ pseudo-spins (here $M = 4$) sequentially coupled to one and the same central spin under the influence of given pulse sequences (quantum gate operations). This architecture could be visualized as a quantum Turing machine with a cyclic ``tape''. Rather than input-output-relations we investigate the resulting process, i.e. the correlation between one- and two-point expectation values (``correlations'') over various time-steps. The resulting spatio-temporal pattern exhibits many non-classical features including Zeno-effects, violation of temporal Bell-inequalities, and quantum parallelism. Due to the strange web of correlations being built-up, specific measurement outcomes for the tape may refer to one or several preparation histories of the head. Specific families of correlation functions are more stable with respect to dissipation than the total wave-function. 
Guenter Mahler and Ilki Kim