On the Monomiality of Nice Error Bases
<|reference_start|>On the Monomiality of Nice Error Bases: 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 (see http://www.imaph.tu-bs.de/qi/problems/6.html) 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 answer is negative. However, we also show that it is always possible to find a fairly sparse representation of a nice error basis.<|reference_end|>
@article{klappenecker2003on,
    title={On the Monomiality of Nice Error Bases},
    author={Andreas Klappenecker (Texas A&M University), Martin Roetteler
  (University of Waterloo)},
    journal={IEEE Transactions on Information Theory, vol. 51, no. 3, pp. 1084
  - 1089, 2005},
    year={2003},
    archivePrefix={arXiv},
    eprint={quant-ph/0301078},
    primaryClass={quant-ph cs.ET}
}