Year: 2003
Type: preprint
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 (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.
Source: arXiv (Cornell University)
Authors: Klappenecker, Andreas, Roetteler, Martin
Institutions: Texas A&M University, University of Waterloo
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2951552189