Probabilistic bisimulations for quantum processes

Modeling and reasoning about concurrent quantum systems is very important for both distributed quantum computing and quantum protocol verification. As a consequence, a general framework formally describing communication and concurrency in complex quantum systems is necessary. For this purpose, we propose a model named qCCS. It is a natural quantum extension of classical value-passing CCS which can deal with input and output of quantum states, and unitary transformations and measurements on quantum systems. The operational semantics of qCCS is given in terms of probabilistic labeled transition system. This semantics has many different features compared with the proposals in the available literature in order to describe the input and output of quantum systems which are possibly correlated with other components. Based on this operational semantics, the notions of strong probabilistic bisimulation and weak probabilistic bisimulation between quantum processes are introduced. Furthermore, some properties of these two probabilistic bisimulations, such as congruence under various combinators, are examined.