Quantum deletion is possible via a partial randomization procedure

Abstract

An alternative kind of deleting/erasing operation is introduced which differs from the commonly used {\it controlled-not} (C-not) conditional logical operation $-$to flip to a standard, `zero' value the (classical or quantum) state of the last copy in a chain, in a deletion process. It is completely reversible, in the classical case, possessing a most natural cloning operation counterpart. We call this deleting procedure R-deletion since, in a way, it can be viewed as a `randomization' of the standard C-not operator. It has the remarkable property of by-passing in a simple manner the `impossibility of deletion of a quantum state' principle, put forward by Pati and Braunstein recently \cite{pbn1}.