Wave-Style Token Machines and Quantum Lambda Calculi (Long Version)

Particle-style token machines are a way to interpret proofs and programs, when the latter are defined according to the principles of linear logic. In this paper, we show that token machines also make sense when the programs at hand are those of a simple linear quantum $\lambda$-calculus. This, however, requires generalizing the concept of a token machine to one in which more than one particle can possibly travel around the term at the same time. This is intimately related to entanglement and allows to give a simple operational semantics to the calculus coherently with the principles of quantum computation.