Unitary invariants of qubit systems

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 kno...

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Vydáno v:Mathematical structures in computer science Ročník 17; číslo 6; s. 1133 - 1151
Hlavní autoři: LUQUE, JEAN-GABRIEL, THIBON, JEAN-YVES, TOUMAZET, FRÉDÉRIC
Médium: Journal Article
Jazyk:angličtina
Vydáno: Cambridge, UK Cambridge University Press 01.12.2007
Cambridge University Press (CUP)
Témata:
Algebra
Algorithms
Computer science
Mathematics
Physics
Polynomials
Quantum Physics
ISSN:0960-1295, 1469-8072
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Shrnutí: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.
Bibliografie:SourceType-Scholarly Journals-1
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ISSN:0960-1295
1469-8072
DOI:10.1017/S0960129507006330