Andreas Klappenecker, Martin Rötteler  Home/Search
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Abstract: Unitary error bases generalize the Pauli matrices to higher dimensional systems. Two basic constructions of unitary error bases are known: An algebraic construction by Knill, which yields nice error bases, and a combinatorial construction by Werner, which yields shift-and-multiply bases. An open problem posed by Schlingemann and Werner relates these two constructions and asks whether each nice error basis is equivalent to a shift-and-multiply basis. We solve this problem and show that the... (Update)
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BibTeX entry: (Update)
@misc{ klappenecker-monomiality,
author = "Andreas Klappenecker and Martin Rötteler",
title = "On the Monomiality of Nice Error Bases",
url = "citeseer.ist.psu.edu/klappenecker03monomiality.html" }
Citations (may not include all citations):21 Finite Groups (context) - Gorenstein - 1980
19 Character Theory of Finite Groups (context) - Isaacs - 1976
9 Nonbinary quantum stabilizer codes - Ashikhmin, Knill - 2001
7 Personal communication (context) - Werner - 2000
6 of Graduate texts in mathematics (context) - Alperin, Bell et al. - 1995
5 All teleportation and dense coding schemes - Werner - 2001
5 Beyond Stabilizer Codes I: Nice Error Bases (context) - Klappenecker, Rotteler - 2002
4 Unitary operator bases (context) - Schwinger - 1960
4 Group representations, error bases and quantum codes - Knill - 1996
3 Transitive linear groups and linear groups which contain irr.. (context) - Hering - 1974
2 Uber die Darstellung endlicher Abelscher Gruppen durch Kolli.. (context) - Frucht - 1931
1 Induced characters which are multiples of irreducible charac.. (context) - Ferguson, Isaacs - 1989
1 Quantum Mechanics - Symbolism of Atomic Measurements (context) - Schwinger - 2001
1 Finite groups with an irreducible representation of large de.. (context) - DeMeyer, Janusz - 1969
1 The Pauli matrices in n dimensions and finest gradings of si.. (context) - Patera, Zassenhaus - 1988
http://www.imaph.tu-bs.de/qi/problems/
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