ua nt - p h / 06 05 18 5 v 1 2 2 M ay 2 00 6 Optimal Fidelity of Deletion

In the recent years many quantum deleting machines are proposed , with varying fidelity of deletion. In this letter we prove that, the fidelity of deletion obtained in [6] , is optimal. Here we have considered a more general transformation and obtained the fidelity of deletion as a function of dot product between two vectors on the Bloch sphere. We show that the maximal value this function can attain is 3 4 which is equal to the fidelity of deletion proposed in [6]. Quantum mechanics plays a vital role in increasing the efficiency of information processing but on the same time provides a restriction on the set of operation which are feasible in digitized information system. Among this set of operations two most important operations are cloning and deletion. Impossibility of such operations are given by two famous theorems 'no-cloning' theorem [1] and 'no-deletion' theorem [2]. However impossibility of such operations does not eradicate the possibility of constructing approximate cloning and deletion machine. Universal cloning machine and many other cloning machines [3] were constructed and it was also proved that the fidelity 5 6 of the Buzek-Hillary cloning machine (Universal Quantum Cloning machine) is the optimal fidelity with which one can clone an unknown quantum state [4]. Approximate deletion machines were also proposed *