It can be represented by two complex numbers, called probability amplitudes ( normalised to 1), that is three real numbers (two polar angles and one radius). Therefore, a single universal U cannot clone a general quantum state. However, this cannot be the case for two arbitrary states. Suppose we have two quantum systems A and B with a common Hilbert space H = H A = H B. However, Ortigoso pointed out in 2018 that a complete proof along with an interpretation in terms of the lack of simple nondisturbing measurements in quantum mechanics was already delivered by Park in 1970. Wootters and Zurek and by Dieks was prompted by a proposal of Nick Herbert for a superluminal communication device using quantum entanglement. 3.1 Mixed states and nonunitary operations Īccording to Asher Peres and David Kaiser, the publication of the 1982 proof of the no-cloning theorem by.This formulation, known as categorical quantum mechanics, allows, in turn, a connection to be made from quantum mechanics to linear logic as the logic of quantum information theory (in the same sense that intuitionistic logic arises from Cartesian closed categories). Together, these underpin the interpretation of quantum mechanics in terms of category theory, and, in particular, as a dagger compact category. The no-cloning theorem has a time-reversed dual, the no-deleting theorem. The no-cloning theorem (as generally understood) concerns only pure states whereas the generalized statement regarding mixed states is known as the no-broadcast theorem. For example, one might use the controlled NOT gate and the Walsh–Hadamard gate to entangle two qubits without violating the no-cloning theorem as no well-defined state may be defined in terms of a subsystem of an entangled state. One should note that the aforementioned theorems do not preclude the state of one system becoming entangled with the state of another as cloning specifically refers to the creation of a separable state with identical factors. The theorem is an evolution of the 1970 no-go theorem authored by James Park, in which he demonstrates that a non-disturbing measurement scheme which is both simple and perfect cannot exist (the same result would be independently derived in 1982 by Wootters and Zurek as well as Dieks the same year). In physics, the no-cloning theorem states that it is impossible to create an independent and identical copy of an arbitrary unknown quantum state, a statement which has profound implications in the field of quantum computing among others.

No clone theorem