Detecting Randomness and Structure in Quantum Processes

Many quantum phenomena—quantum communication protocols, blinking quantum dots, cavity QED sources—generate sequential entangled qudits, which we call quantum stochastic processes. In an effort to understand their information content and correlation, we develop a framework for stationary, ergodic quantum processes and define quantum information properties related to the von Neumann entropies of sequential qudit blocks. Qudit blocks can exhibit both purely-classical and uniquely-quantum correlations. Applying sequential measurements yields classical stochastic processes whose informational properties are bounded by those of the underlying quantum process. The type of measurement—projective or POVM, single- or joint-qudit basis, fixed basis or adaptive measurement protocol—determine how structured the underlying process appears to an experimenter whose only access is via measurements. We detail examples with short- and long-range entanglement, as well as a variety of correlational structures determined by specific Hamiltonian dynamics.