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arXiv:quant-ph/0605173

Stronger no-cloning, no-signalling and conservation of quantum information

Indranil Chakrabarty, Arun Kumar Pati, Satyabrata Adhikari

Published May 19, 2006• 0 citations
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Abstract

It is known that the stronger no-cloning theorem and the no-deleting theorem taken together provide the permanence property of quantum information. Also, it is known that the violation of the no-deletion theorem would imply signalling. Here, we show that the violation of the stronger no-cloning theorem could lead to signalling. Furthermore, we prove the stronger no-cloning theorem from the conservation of quantum information. These observations imply that the permanence property of quantum information is connected to the no-signalling and the conservation of quantum information.

DOI
10.48550/arxiv.quant-ph/0605173

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It is known that the stronger no-cloning theorem and the no-deleting theorem taken together provide the permanence property of quantum information. Also, it is known that the violation of the no-deletion theorem would imply signalling. Here, we show that the violation of the stronger no-cloning theorem could lead to signalling. Furthermore, we prove the stronger no-cloning theorem from the conservation of quantum information. These observations imply that the permanence property of quantum information is connected to the no-signalling and the conservation of quantum information.
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.
Over the past decade, quantum information theory has developed into a vigorous field of research despite the fact that quantum information, as a precise concept, is undefined. Indeed, the very idea of viewing quantum states as carriers of some kind of information (albeit unknowable in classical terms) leads naturally to interesting questions that might otherwise never have been asked, and corresponding new insights. We discuss some illustrative examples, including a strengthening of the well-known no-cloning theorem leading to a property of permanence for quantum information, and considerations arising from information compression that reflect on fundamental issues.
Heisenberg's uncertainty principle and recently derived many no-go theorems including the no-cloning theorem and the no-deleting theorem have corroborated the idea that we can never access quantum information without causing disturbance. Here we disprove this presumption by predicting a novel phenomenon, `quantum catalysis of information,' where a system enables an otherwise impossible task by exchanging information through a quantum communication channel. This fact implies that making use of quantum information does not always cause disturbance.