Abstract
The no-cloning theorem states that an arbitrary quantum state cannot be copied from one qubit and duplicated on another qubit. We offer a proof of this theorem and illustrate how quantum states can be teleported between two qubits. The Bell and Clauser-Horne-Shimony-Holt inequalities are introduced and shown to be demonstrable features of entangled quantum systems. We discuss how the private key distribution problem is dealt with using quantum key distribution (QKD). The BB84 and Ekert protocols are examples of the latter, and we review and illustrate their implementation. We show how entangled states enable dense coding and offer a brief synopsis of Greenberger-Horne-Zeilinger GHZ states and their application.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
Correlation experiments where anticipated by Chien-Shiung Wu as early as 1950 [12].
- 2.
As you might guess from the film’s title, things did not work out well for our anti-hero.
- 3.
Flying qubits are physically transported between two locations. Typically they are photons traveling through empty space or some medium.
- 4.
Two points in space-time that cannot be bridged by a light-beam, or anything moving less than the speed of light.
References
A. Aspect, P. Grangier, G. Roger, Physical Review Letters 49, 91 1982
J. S. Bell, Speakable and Unspeakable in Quantum Mechanics, Cambridge University Press 1987
J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, Physical Review Letters 23, 880 1969
M. Giustina et al., https://doi.org/10.1103/PhysRevLett.115.250401
D. M. Greenberger, M.A. Horne, A. Zeilinger, 2007arXiv0712.0921G, (2007)
B. Hensen et al., https://doi.org/10.1038/nature15759
Michael E. Nielsen and Isaac L. Chuang, Quantum Computation and Quantum Information, Cambridge U. Press, 2011
C. Pacher, A. Abidin, T. Lörunser, M. Peev, R. Ursin, A. Zeilinger, J. Larsson, Quantum Information Processing, 15, 327 2016
Stephen Hawking and Roger Penrose, The Nature of Space and Time, (Princeton U. Press 1996) pg. 121
L. K. Shalm et al., https://doi.org/10.1103/PhysRevLett.115.250402
A. Shimony, in The Stanford Encyclopedia of Philosophy ed. by Edward N. Zalta (Fall 2017 Edition), https://plato.stanford.edu/archives/fall2017/entries/bell-theorem/
C. S. Wu and I. Shaknov, Phys. Rev. 77, 136 1950
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Zygelman, B. (2018). No-Cloning Theorem, Quantum Teleportation and Spooky Correlations. In: A First Introduction to Quantum Computing and Information. Springer, Cham. https://doi.org/10.1007/978-3-319-91629-3_6
Download citation
DOI: https://doi.org/10.1007/978-3-319-91629-3_6
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-91628-6
Online ISBN: 978-3-319-91629-3
eBook Packages: Computer ScienceComputer Science (R0)