Quantum mechanical Universal constructor

Arbitrary quantum states cannot be copied. In fact, to make a copy we must provide complete information about the system. However, can a quantum system self-replicate? This is not answered by the no-cloning theorem. In the classical context, Von Neumann showed that a ‘universal constructor’ can exist which can self-replicate an arbitrary system, provided that it had access to instructions for making copy of the system. We question the existence of a universal constructor that may allow for the self-replication of an arbitrary quantum system. We prove that there is no deterministic universal quantum constructor which can operate with finite resources. Further, we delineate conditions under which such a universal constructor can be designed to operate dterministically and probabilistically. The basis of classical computation is the Church-Turing thesis [1,2] which says that every recursive function can be computed algorithmically provided the algorithm can be executed by a physical process. However, fundamental physical processes are not governed by classical mechanics, rather by quantum mechanical laws. The possibility of performing reversible computation [3] and the fact that classical computers cannot efficiently simulate quantum systems [4,5] gave birth to the concept of the quantum Turing machine [6]. This led to a flurry of discoveries in quantum computation [7], quantum algorithms [8–11], quantum simulators [12], quantum automaton [13] and programmable gate array [14]. In another development, von Neumann [15] thought of an extension of the logical concept of a universal computing machine which might mimic a living system. One of the hall-mark properties of a living system is its capability of self-reproduction. He asked the question: Is it possible to design a machine that could be programmed to produce a copy of itself, in the same spirit that a Turing machine can be programmed to compute any function allowed by physical law. More precisely, he defined a ‘universal constructor’ as a machine which can reproduce itself if it is provided with a program containing its own description. The process of selfreproduction requires two steps: first, the constructor has to produce a copy of itself and second, it has to produce the program of how to copy itself. The second step is important in order that the self-reproduction continues, otherwise, the child copy cannot self-reproduce. When the constructor produces a copy of the program, then it attaches it to the child copy and the process repeats. Unexpectedly, working with classical cellular automaton it was