The monomial representations of the Clifford group
D.M. Appleby, Ingemar Bengtsson, Stephen Brierley, Markus Grassl,, David Gross, Jan-{\AA}ke Larsson
TL;DR
This paper demonstrates that the Clifford group can be represented by monomial matrices only in square dimensions, simplifying SIC vector expressions and providing new solutions in dimension 16.
Contribution
It establishes a condition for monomial representations of the Clifford group and presents the first exact SIC solutions in dimension 16.
Findings
Clifford group has monomial representations only in square dimensions
Simplifies expressions for SIC vectors and related structures
Provides the first exact SIC solutions in dimension 16
Abstract
We show that the Clifford group - the normaliser of the Weyl-Heisenberg group - can be represented by monomial phase-permutation matrices if and only if the dimension is a square number. This simplifies expressions for SIC vectors, and has other applications to SICs and to Mutually Unbiased Bases. Exact solutions for SICs in dimension 16 are presented for the first time.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.