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Unitary invariants of qubit systems

Published online by Cambridge University Press:  01 December 2007

JEAN-GABRIEL LUQUE ,
JEAN-YVES THIBON  and
FRÉDÉRIC TOUMAZET
JEAN-GABRIEL LUQUE
Affiliation:
Institut Gaspard Monge, Université de Marne-la-Vallée, F-77454 Marne-la-Vallée cedex, France Email: luque@univ-mlv.fr, jyt@univ-mlv.fr
JEAN-YVES THIBON
Affiliation:
Institut Gaspard Monge, Université de Marne-la-Vallée, F-77454 Marne-la-Vallée cedex, France Email: luque@univ-mlv.fr, jyt@univ-mlv.fr
FRÉDÉRIC TOUMAZET
Affiliation:
Laboratoire d'Informatique de Paris Nord, Institut Galilée-Université Paris 13/Paris Nord, 99 av. J.-B. Clement 93430 Villetaneuse, France Email: ft@lipn.univ-paris13.fr
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Abstract

We give an algorithm allowing the construction of bases of local unitary invariants of pure k-qubit states from a knowledge of the polynomial covariants of the group of invertible local filtering operations. The simplest invariants obtained in this way are made explicit and compared with various known entanglement measures. Complete sets of generators are obtained for up to four qubits, and the structure of the invariant algebras is discussed in detail.

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 17 , Issue 6 , December 2007 , pp. 1133 - 1151
Copyright
Copyright © Cambridge University Press 2007

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