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Cloning in C *-Algebras

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

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 (kanio@math.uni.lodz.pl; lubnauer@math.uni.lodz.pl; anluczak@math.uni.lodz.pl)
Katarzyna Lubnauer
Affiliation:
Faculty of Mathematics and Computer Science, Łódź University, ulica Stefana Banacha 22, 90-238 Łódź, Poland (kanio@math.uni.lodz.pl; lubnauer@math.uni.lodz.pl; anluczak@math.uni.lodz.pl)
Andrzej Łuczak
Affiliation:
Faculty of Mathematics and Computer Science, Łódź University, ulica Stefana Banacha 22, 90-238 Łódź, Poland (kanio@math.uni.lodz.pl; lubnauer@math.uni.lodz.pl; anluczak@math.uni.lodz.pl)
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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

Information

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 

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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