Quantum Zenon effects are discussed in terms of a specific class of quantum trajectories, which are conditioned by continuous, mutually exclusive measurement signals. Such a conditioning is not restricted to simple systems but can be generalized to composite networks. In any case, the characteristic features of these trajectories tend to be washed out in the ensemble limit and thus require single system analysis. Only on a sufficiently small time-scale and for a coherent initial state, also the ensemble exhibits some Zenon effect. In this case, ironically, actual measurements are not required: a closed single composite system can emulate this behavior. Such a kind of quantum parallelism underlies also recent proposals for quantum computation.

Based on the SU ( n )-algebra the Markoff master equation in discrete product space is reformulated to explicitly deal with composite systems. The resulting local (single node) and nonlocal (multi-node) state parameters allow a systematic approach to non-classical features of the state, like variance and covariance tensors. For local optical driving forces, inter-node interactions, and local damping channels the solution of the master equation is unraveled into stochastic quantum trajectories. Sampling leads to a joint distribution function in terms of those state parameters. Its linear moments define the ensemble-density matrix. The average variance and covariance are in terms of non-linear moments, which should be distinguished from their entirely statistical counterpairs. Non-classicality of the network dynamics is shown to reflect itself in the luminescence-photonstatistics.

Quantum networks might optically be controlled to map non-classical features in their time-evolution onto entanglement between its subsystems. ''Projections without dissipation'' support the view that history traces are consistently defined only on the time scale of repeated measurements; without dissipation temporal Bell inequalities tend to be violated.

A simple quantum network consisting of up to four SU(2)-nodes (spin-1/2 subsystems) is studied to model explicitly the dynamics of quantum measurement processes. The resulting stochastic dynamics is simulated by the Monte Carlo wavefunction approach (MCWA) extended to composite few-particle systems. It is shown that the main features of axiomatic measurement theory can be recovered within this model, e.g. the dynamical emergence of projections. the superposition of undecidable alternatives. Exploiting the superposition of undecidable paths it is shown that EPR and GHZ states can be prepared within these quantum networks as attractor states.

Nanostructures might be viewed as solid-state approximations to SU(N) networks, the nodes of which would, in simplest form, be analogous to elementary spins. Owing to interactions with an external light field and coupling between the local nodes these networks allow for single- and multiple-node coherence (entanglement), despite damping. By means of stochastic simulations we demonstrate how such a ‘quantum machinery’ embedded in a qualified environment would look like in terms of measurement protocols. These protocols give evidence for the underlying complex behaviour of the network, a complexity which is based on the non-local information contained in the entanglement and which would not be present in the ‘classical limit’ of using local information only.