The linked paper says in the abstract: The calculus turns out to be closely related to the linear lambda calculi used in the study of Linear Logic. We set up a

The linked paper says in the abstract: The calculus turns out to be closely related to the linear lambda calculi used in the study of Linear Logic. We set up a computational model and an equational proof system for this calculus, and we argue that it is equivalent to the quantum Turing machine.