From Reversible to Irreversible Computations

In this paper we study the relation between reversible and irreversible computation applicable to different models of computation — here we are considering classical and quantum computation. We develop an equational theory of reversible computations and an associated theory of irreversible computations which is obtained by marking some inputs as preinitialised heap and some outputs as garbage to be thrown away at the end of the computation. We present three laws which apply to irreversible classical and quantum computations and show that von Neumann's measurement postulate is derivable from them. We discuss the question whether these laws are complete for irreversible quantum computations.