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Revista Brasileira de Ensino de Física

A remark on quantum cloning

Christian DE RONDE, Massimiliano Sassoli de Bianchi

Published Jan 1, 2019• 0 citations
Publisher

Abstract

Physical entities are not truly teleported in so-called quantum teleportation, only their states are. Similarly, physical entities are not truly cloned in so-called quantum cloning, only their states are. The celebrated no-cloning theorem tells us that a universal cloning machine, able to perfectly clone arbitrary states, cannot be built. However, this only applies to discernible quantum entities. For the indiscernible ones, which are already perfect clones of one another, the additional cloning of their state is in fact a natural process, which happens in a spontaneous way, as soon as they are allowed to interact.

DOI
10.1590/1806-9126-rbef-2019-0033

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Physical entities are not truly teleported in so-called quantum teleportation, only their states are. Similarly, physical entities are not truly cloned in so-called quantum cloning, only their states are. The celebrated no-cloning theorem tells us that a universal cloning machine, able to perfectly clone arbitrary states, cannot be built. However, this only applies to discernible quantum entities. For the indiscernible ones, which are already perfect clones of one another, the additional cloning of their state is in fact a natural process, which happens in a spontaneous way, as soon as they are allowed to interact.
The impossibility of cloning an unknown quantum state is one of the basic rules governing quantum physics.This statement, known as the "no-cloning theorem", prohibits perfect cloning, but doesn't oppose approximate copying.In this paper, we will prove that, due to the uncontrollable quantum fluctuations, no perfect cloning can be achieved.Such a situation allows us to treat the no-cloning theorem as an equivalent one to Leibniz's principle, and further unify them under the notion of uniqueness; that is, any physical entities (whether macroscopic or microscopic objects) in nature would have its individuality.Moreover, we also demonstrate the universality of unique scheme by showing that, any process of trying to construct one exactly symmetrical or asymmetrical body of a physical object is forbidden.On the whole, nature doesn't allow the existence of completely identical, symmetrical or asymmetrical things and this conclusion is valid for all physical domains.
Quantum theory fundamentally forbids the perfect copying of an arbitrary unknown quantum state, according to a principle known as the no-cloning theorem. Nevertheless, it is possible to construct a deterministic quantum map that produces multiple approximate copies of an unknown quantum state. This task is referred to as universal quantum cloning, further facilitating numerous quantum technologies such as quantum cryptography and quantum communication. In this work, we theoretically verify that the universal quantum cloning cannot be realized within a noncontextual theory, highlighting its intrinsically nonclassical nature. Our verification first {focuses on revealing that} 1→21\rightarrow21→2 cloning scenario {is fully contextual}, and {further covers general examples to observe the contextual behavior of} N→MN\rightarrow MN→M scenario. We believe that our results regarding quantum cloning serve a key role for understanding both quantum foundation and application.
Quantum teleportation, a cornerstone of quantum information science, allows for the transfer of an unknown quantum state without physically moving the associated quantum particle. This process critically relies on shared entanglement and classical communication. A fundamental aspect of quantum information is the no-cloning theorem, which dictates that an arbitrary unknown quantum state cannot be perfectly copied. This paper investigates the intrinsic connection between Bell nonlocality, a profound manifestation of quantum entanglement, and the inherent unclonability of quantum teleportation. We argue that the very existence of Bell nonlocality within the shared entangled resource not only enables quantum teleportation but also fundamentally guarantees that the teleported state cannot be perfectly cloned. By examining the theoretical underpinnings of Bell's theorem and the quantum teleportation protocol, we demonstrate how the non-local correlations preclude any possibility of state duplication, thereby upholding the no-cloning theorem. This connection is vital for understanding the security and foundational aspects of quantum communication, establishing Bell nonlocality as a strong certification of secure, non-duplicable quantum state transfer. The analysis highlights that successful quantum teleportation, intrinsically linked to the violation of Bell inequalities, provides an experimental signature of the non-classical correlations that underpin security against cloning.
Due to the Heisemberg uncertainty principle, it is impossible to design a procedure which permits perfect cloning of an arbitrary, unknown "qubit" (the spin or polarization state of a single quantum system)1,2. However, it is believed that a perfect copying protocol can be achieved, at least in principle, if the qubit to be copied is destroyed in the original system. Quantum teleportation3,4 is supposed to allow for such a result. Here, this belief is shown to be invalidated by a fundamental uncertainty about the number of particles involved in any process, as predicted by Quantum Field Theory. As a result, teleportation cannot provide an infallible copying procedure for the single qubits, not even in the limit of perfect experimental sensitivities. The no-cloning theorem1,2 can then be generalized to the case of destroying the original. Teleportation remains an interesting statistical procedure, having an unavoidable theoretical error at the percent level or few orders of magnitude smaller, depending on the physical process that is used. Although it cannot be made arbitrarily small, such an error is small enough to remain hidden in present experiments.
This chapter begins by providing proofs of no-cloning and no-broadcasting theorems. No-cloning theorem makes it possible to detect any eavesdropper on a quantum communication channel. The chapter presents the features of some of the quantum cloning machines. In spite of the no-cloning theorem, it is quite possible to construct a quantum cloning machine which copies an unknown state approximately. A probabilistic cloning machine has been proposed which can succeed only with a probability. When it succeeds it will give a perfect copy. This probabilistic quantum cloning is much useful in studying the B92 quantum key distribution protocol which involves only two non-orthogonal states and we can try to clone it with the largest probability. A telecloning scheme combines cloning with teleportation. A quantum telecloning system for two-level system in which one input is sent to M-receivers has been proposed. The no-hiding theorem is found to have applications in black hole evaporation, quantum teleportation and private quantum channels.