Delocalized and dynamical catalytic randomness and information flow

We generalize the theory of catalytic quantum randomness to distributed and dynamical settings. First, we expand the theory of catalytic quantum randomness by calculating the amount of (Renyi) entropy catalytically extractable from a distributed or dynamical randomness source. We show that no entropy can be catalytically extracted when one cannot implement local projective measurement on randomness source without altering its state. As an application, we prove that quantum operation cannot be hidden in correlation between two parties without using randomness, which is the dynamical generalization of the no-hiding theorem. Moreover, the formalism of distributed catalysis is applied to develop a formal definition of semantic quantum information and it follows that utilizing semantic information is equivalent to catalysis using a catalyst already correlated with the transforming system. By doing so, we unify the utilization of semantic and nonsemantic quantum information and conclude that one can always extract more information from an incompletely depleted classical randomness source, but it is not possible for quantum randomness sources.

Automated summary

We generalize the theory of catalytic quantum randomness to distributed and dynamical settings. The theory is expanded by calculating the amount of entropy extractable catalytically from a distributed or dynamical randomness source, and it is demonstrated that no entropy can be catalytically extracted when one cannot implement local projective measurement on the randomness source without altering its state. Applications include proving that quantum operations cannot be hidden in correlations between two parties without using randomness, and developing a formal definition of semantic quantum information using the formalism of distributed catalysis. It is concluded that more information can always be extracted from an incompletely depleted classical randomness source, but this is not possible for quantum randomness sources.