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How to Beat Restrictions Imposed by no-Cloning Theorem and Relativity Theory?

Dhananjay P. Mehendale

Published Feb 1, 2014• 0 citations
OpenAlex

Abstract

We suggest a way to produce any number of clones of an unknown quantum state. We also suggest a way to transmit information from one place to other far away place exactly and almost instantaneously. This paper thus aims to suggest a method to produce “more than one clone” and a method to achieve “instantaneous and exact information transfer”.

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Linearly-independent quantum states can be cloned

L.-M. Duan, Guang‐Can Guo

A fundamental question in quantum mechanics is, whether it is possible to replicate an arbitrary unknown quantum state. Then famous quantum no-cloning theorem [Nature 299, 802 (1982)] says no to the question. But it leaves open the following question: If the state is not arbitrary, but secretly chosen from a certain set $\$={ | Ψ_1> ,| Ψ_2> ,... ,| Ψ_n> } $, whether is the cloning possible? This question is of great practical significance because of its applications in quantum information theory. If the states $| Ψ_1>, | Ψ_2>,...$ and $| Ψ_n> $ are linearly-dependent, similar to the proof of the no-cloning theorem, the linearity of quantum mechanics forbids such replication. In this paper, we show that, if the states $| Ψ_1>, | Ψ_2>, ...$ and $| Ψ_n> $ are linearly-independent, they do can be cloned by a unitary-reduction process.

arXiv:quant-ph/9705018•May 12, 1997•2 citations
We suggest a way to produce any number of clones of an unknown quantum state. We also suggest a way to transmit information from one place to other far away place exactly and almost instantaneously. This paper thus aims to suggest a method to produce “more than one clone” and a method to achieve “instantaneous and exact information transfer”.
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.
It is well known that (non-orthogonal) pure states cannot be cloned so one may ask: how much or what kind of additional (quantum) information is needed to supplement one copy of a quantum state in order to be able to produce two copies of that state by a physical operation? For classical information, no supplementary information is required. However for pure quantum (non-orthogonal) states, we show that the supplementary information must always be as large as it can possibly be i.e. the clone must be able to be generated from the additional information alone, independently of the first (given) copy.
To a certain extend experimental quantum teleportation has been demonstrated. A minimal scheme to teleport an unknown quantum multiple times is described which can be used for chaining of quantum teleportation. The scheme is combined with results from special relativity. A conventional idealized computation is conducted which would yield the predictions that it would be possible to teleport with given idealized probability an unknown quantum state to a point in spacetime which is, e.g., slightly within the past of the starting point. Conducting this scheme in a certain way multiple times would lead to the idealized predictions that multiple special kinds of perfect clones of an unknown quantum state can be obtained with given probability. A feature of such clones is elucidated according to which one may call them ‘dependent’ clones. The results are in accordance with the no-cloning theorem, because the clones would be generated only with given idealized probability, and, of course, using this scheme classical information cannot be transmitted superluminal, and it cannot be transmitted into the past. Quantum states, idealized probabilities for the different possible states, and parameters for the experiments are computed.
A fundamental question in quantum mechanics is, whether it is possible to replicate an arbitrary unknown quantum state. Then famous quantum no-cloning theorem [Nature 299, 802 (1982)] says no to the question. But it leaves open the following question: If the state is not arbitrary, but secretly chosen from a certain set $$={ | Ψ_1> ,| Ψ_2> ,... ,| Ψ_n> } $, whether is the cloning possible? This question is of great practical significance because of its applications in quantum information theory. If the states ∣Ψ1>,∣Ψ2>,...| Ψ_1>, | Ψ_2>,...∣Ψ1​>,∣Ψ2​>,... and $| Ψ_n> $ are linearly-dependent, similar to the proof of the no-cloning theorem, the linearity of quantum mechanics forbids such replication. In this paper, we show that, if the states ∣Ψ1>,∣Ψ2>,...| Ψ_1>, | Ψ_2>, ...∣Ψ1​>,∣Ψ2​>,... and $| Ψ_n> $ are linearly-independent, they do can be cloned by a unitary-reduction process.