Limits on quantum deletion from no signaling principle

One of the fundamental restrictions that quantum mechanics imposes is the "No deletion Theorem" which tells us that given two identical unknown quantum states, it is impossible to delete one of them. But nevertheless if not perfect, people have tried to delete it approximately. In these approximate deleting processes our basic target is to delete one of the two identical copies as much as possible while preserving the other copy. In this brief report, by using the No communication theorem (NCT) (impossibility of sending signal faster than light using a quantum resource) as a guiding principle, we obtain a bound on the sum of the fidelity of deletion and the fidelity of preservation. Our result not only brings out the complementary relation between these two fidelities but also predicts the optimal value of the fidelity of deletion achievable for a given fidelity of preservation under no signaling constraint. This work eventually saturates the quest for finding out the optimal value of deletion within the NCT framework.