Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-05T02:51:56.514Z Has data issue: false hasContentIssue false
  • English
  • Français

Cloning in C*-Algebras

Part of: Groups and algebras in quantum theory Selfadjoint operator algebras

Published online by Cambridge University Press:  15 December 2016

Krzysztof Kaniowski ,
Katarzyna Lubnauer  and
Andrzej Łuczak
Krzysztof Kaniowski
Affiliation:
Faculty of Mathematics and Computer Science, Łódź University, ulica Stefana Banacha 22, 90-238 Łódź, Poland ([email protected]; [email protected]; [email protected])
Katarzyna Lubnauer
Affiliation:
Faculty of Mathematics and Computer Science, Łódź University, ulica Stefana Banacha 22, 90-238 Łódź, Poland ([email protected]; [email protected]; [email protected])
Andrzej Łuczak
Affiliation:
Faculty of Mathematics and Computer Science, Łódź University, ulica Stefana Banacha 22, 90-238 Łódź, Poland ([email protected]; [email protected]; [email protected])
Get access Rights & Permissions [Opens in a new window]

Abstract

Cloneable sets of states in C*-algebras are characterized in terms of strong orthogonality of states. Moreover, the relation between strong cloning and distinguishability of states is investigated together with some additional properties of strong cloning in abelian C*-algebras.

Keywords

cloning statesC*-algebrasvon Neumann algebrasthe universal representation

MSC classification

Secondary: 46L30: States 81R15: Operator algebra methods 81P50: Quantum state estimation, approximate cloning
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 60 , Issue 3 , August 2017 , pp. 689 - 705
Copyright
Copyright © Edinburgh Mathematical Society 2016 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Barnum, H., Caves, C. M., Fuchs, C. A., Jozsa, R. and Schumacher, B., Noncommuting mixed states cannot be broadcast, Phys. Rev. Lett. 76(15) (1996), 2818–2821.Google Scholar
2. Barnum, H., Barrett, J., Leifer, M. and Wilce, A., Cloning and broadcasting in generic probability models, Preprint (arXiv:quant-ph/0611295; 2006).Google Scholar
3. Barnum, H., Barrett, J., Leifer, M. and Wilce, A., Generalized no-broadcasting theorem, Phys. Rev. Lett. 99 (2007), 240501.Google Scholar
4. Bratteli, O. and Robinson, D. W., Operator Algebras and Quantum Statistical Mechanics, Volume I (Springer, 1979).Google Scholar
5. Clifton, R., Bub, J. and Halvorson, H., Characterizing quantum theory in terms of information-theoretic constraints, Foundations Phys. 33 (2003), 1561–1591.Google Scholar
6. Dieks, D., Communication by EPR devices, Phys. Lett. A92(6) (1982), 271–272.Google Scholar
7. Kadison, R. V. and Ringrose, J. R., Fundamentals of the Theory of Operator Algebras, Volume II (Academic Press, 1986).Google Scholar
8. Kaniowski, K., Lubnauer, K. and Łuczak, A., Cloning and broadcasting in operator algebras, Q. J. Math. 66(1) (2015), 191–212.Google Scholar
9. Lindblad, G., A general no-cloning theorem, Lett. Math. Phys. 47 (1999), 189–196.CrossRefGoogle Scholar
10. Łuczak, A., Cloning by positive maps in von Neumann algebras, Positivity 19(2) (2015), 317–332.CrossRefGoogle Scholar
11. Takesaki, M., Theory of Operator Algebras I (Springer, 1979).CrossRefGoogle Scholar
12. Wooters, W. K. and Zurek, W. H., A single quantum state cannot be cloned, Nature 299 (1982), 802.CrossRefGoogle Scholar