Relatively Random Unitary Operators

Życzkowski, Karol

doi:10.1007/978-3-0348-8545-4_33

Karol Życzkowski⁶

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 70))

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Abstract

Consider unitary operators Û₁ and Û₂ represented by matrices U ₁ and U ₂ of size N. We shall call operators Û₁ and Û₂ relatively random. if

$$ \mu = \frac{{\operatorname{Re} \left[ {Tr(U_1^\dag U_2^\dag {U_1}{U_2})} \right]}}{N} \ll 1. $$

((1))

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Authors and Affiliations

Instytut Fizyki, Uniwersytet Jagielloński, ul. Reymonta 4, 30-059, Kraków, Poland
Karol Życzkowski

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Karol Życzkowski
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Editors and Affiliations

Technische Universität Clausthal, Institut für Mathematik, Erzstrasse 1, D-38678, Clausthal-Zellerfeld, Germany
M. Demuth
Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Head Post Office Box 79, Moscow, Russia
P. Exner
Fachbereich Mathematik MA 7-2, Technische Universität Berlin, Strasse des 17. Juni 136, D-10623, Berlin, Germany
H. Neidhardt
Université d’Aix-Marseille II et, Centre de Physique Théorique, CNRS — Luminy — Case 907, F-13288, Marseille Cedex 9, France
V. Zagrebnov

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Życzkowski, K. (1994). Relatively Random Unitary Operators. In: Demuth, M., Exner, P., Neidhardt, H., Zagrebnov, V. (eds) Mathematical Results in Quantum Mechanics. Operator Theory: Advances and Applications, vol 70. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8545-4_33

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DOI: https://doi.org/10.1007/978-3-0348-8545-4_33
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9673-3
Online ISBN: 978-3-0348-8545-4
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