The limited role of mutually unbiased product bases in dimension 6

2011/11/30 by Daniel McNulty, Stefan Weigert
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Basis (linear algebra) #Combinatorics #Computer science #Dimension (graph theory) #Finite Group Theory Research #Geometry #Mathematics #Mutually unbiased bases #Polynomial and algebraic computation #Product (mathematics) #Set (abstract data type) #graph theory and CDMA systems #quant-ph

paper · pdf · doi:10.1088/1751-8113/45/10/102001

published as J. Phys. A: Math. Theor. 45 (2012) 102001 · 8 pages, identical to published version

openalex publication_date 2012/02/21 · arxiv created 2012/03/12 · arxiv updated 2012/03/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We show that a complete set of seven mutually unbiased bases in dimension six, if it exists, cannot contain more than one product basis.

Citations

• Mubs and Hadamards of Order Six
• Security of Quantum Key Distribution Usingd-Level Systems
• Structure of the sets of mutually unbiased bases forNqubits
• Mutually unbiased bases and semi-definite programming
• Constructing mutually unbiased bases in dimension six
• Numerical evidence for the maximum number of mutually unbiased bases in dimension six
• Mutually unbiased bases for continuous variables