Quantum superposition of multiple clones and the novel cloning machine

The quantum world is certainly different from the classical world where one can have linear superposition of all possibilities with appropriate probabilities. We ask if a real quantum cloning machine exists then it should exploit this basic feature of the quantum world and it should produce simultaneously 1 to 2, 1 to 3, and 1 to M copies. Is it really possible by some physical process to produce an output state of an unknown quantum state which will be in a linear superposition of all possible multiple copies? If such a device exists we would call it an ideal “novel quantum cloning machine” (NQCM). However, such an ideal novel cloning machine can not exist. So, we envisage a novel quantum cloning machine, which takes an input state and produces an output state whose success branch can exist in a linear superposition of multiple copies of the input state and the failure branch exist in a superposition of composite state independent of the input state. We prove that unknown non-orthogonal states chosen from a set S can evolve into a linear superposition of multiple clones by a unitary process if and only if the states are linearly independent. We derive a bound on the success probability of the novel cloning machine. We argue that the deterministic and probabilistic clonings are special cases of our novel cloning machine. PACS NO: 03.67.Hk, 03.65.Bz email:[email protected] The information theoretical approach to the foundations of quantum theory is to regard the debatable issues as facts of the quantum world and to exploit these facts in a constructive way so as to achieve classically forbidden technological applications in quantum information processing. In recent years the quantum mechanical principles such as linearity, unitarity and inseparability have been utilised to realise quantum computers [1], quantum teleportation [2], quantum cryptography [3] and so on. In one hand these principles enhance the possibility of information processing and on the other they put some limitations, too. That an unknown quantum state can not be perfectly copied is a consequence of linearity of quantum theory. This was realised by Wootters-Zurek [4] and Dieks [5]. Interestingly, Susskind and Uglun [6] have invoked the quantum “no-cloning” theorem to explain the information loss in side a