No-cloning Theorem and Quantum Copying

Quantum Mechanics for Beginners ◽

10.1093/oso/9780198854227.003.0011 ◽

2020 ◽

pp. 172-181

Author(s):

M. Suhail Zubairy

Keyword(s):

Quantum Mechanics ◽

Quantum State ◽

Uncertainty Relation ◽

Foundations Of Quantum Mechanics ◽

Quantum Cloning ◽

Foundation Of Quantum Mechanics ◽

Quantum Copying ◽

Arbitrary Quantum ◽

Principle Of Complementarity

Heisenberg’s uncertainty relation and Bohr’s principle of complementarity form the foundations of quantum mechanics. If these are violated then the edifice of quantum mechanics can come crashing down. In this chapter, it is shown how cloning or perfect copying of a quantum state can potentially lead to a violation of these sacred principles. A no-cloning theorem is proven showing that the cloning of an arbitrary quantum state is not allowed. The foundation of quantum mechanics is therefore protected. It is also shown how quantum cloning can lead to superluminal communication. It is also discussed that, if making a perfect copy of a quantum state is forbidden, how best a copy of a state can be made.

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Quantum Mechanics for Beginners

10.1093/oso/9780198854227.001.0001 ◽

2020 ◽

Author(s):

M. Suhail Zubairy

Keyword(s):

High School ◽

Quantum Mechanics ◽

Quantum Computing ◽

Quantum Communication ◽

Foundations Of Quantum Mechanics ◽

Quantum Superposition ◽

Quantum Dense Coding ◽

Foundation Of Quantum Mechanics ◽

Wave Particle Duality ◽

And Mathematics

Quantum mechanics is a highly successful yet a mysterious theory. Quantum Mechanics for Beginners provides an introduction of this fascinating subject to someone with only a high school background in physics and mathematics. This book, except the last chapter on the Schrödinger equation, is entirely algebra-based. A major strength of this book is that, in addition to the foundation of quantum mechanics, it provides an introduction to the fields of quantum communication and quantum computing. The topics covered include wave–particle duality, the Heisenberg uncertainty relation, Bohr’s principle of complementarity, quantum superposition and entanglement, Schrödinger’s cat, Einstein–Podolsky–Rosen paradox, Bell theorem, quantum no-cloning theorem and quantum copying, quantum eraser and delayed choice, quantum teleportation, quantum key distribution protocols such as BB-84 and B-92, counterfactual communication, quantum money, quantum Fourier transform, quantum computing protocols including Shor and Grover algorithms, quantum dense coding, and quantum tunneling. All these topics and more are explained fully but using only elementary mathematics. Each chapter is followed by a short list of references and some exercises. This book is meant for an advanced high school student and a beginning college student and can be used as a text for a one semester course at the undergraduate level. However it can also be a useful and accessible book for those who are not familiar but want to learn some of the fascinating recent and ongoing developments in areas related to the foundations of quantum mechanics and its applications to quantum communication and quantum computing.

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