On mutually unbiased unitary bases in prime-dimensional Hilbert spaces

• Main Authors: Nasir, Rinie N. M., Shamsul Shaari, Jesni, Mancini, Stefano
• Format: Article
• Language: English; English; English
• Published: Springer US 2019
• Subjects: QA155 Algebra; QC Physics
• Online Access: http://irep.iium.edu.my/71981/1/71981_On%20mutually%20unbiased%20unitary.pdf; http://irep.iium.edu.my/71981/7/71981%20On%20mutually%20unbiased%20unitary%20bases%20%20SCOPUS.pdf; http://irep.iium.edu.my/71981/13/71981_On%20mutually%20unbiased%20unitary%20bases%20in%20prime-dimensional%20Hilbert%20spaces_wos.pdf; http://irep.iium.edu.my/71981/; https://link.springer.com/article/10.1007/s11128-019-2298-2
• Institution: Universiti Islam Antarabangsa Malaysia

Akin to the idea of complete sets of mutually unbiased bases for prime-dimensional Hilbert spaces, Hd, we study its analogue for a d-dimensional subspace of M(d,C), i.e. mutually unbiased unitary bases (MUUBs) comprising of unitary operators. We note an obvious isomorphism between the vector spaces and beyond that, we define a relevant monoid structure for Hd isomorphic to one for the subspace of M(d,C). This provides us not only with the maximal number of such MUUBs, but also a recipe for its construction.