On Obtaining New MUBs by Finding Points on Complete Intersection Varieties over

Authors

• Arindam Banerjee, Indian Institute of Technology Kharagpur
• Kanoy Kumar Das, Ramakrishna Mission Vivekananda Educational and Research Institute
• Ajeet Kumar, Indian Statistical Institute, Kolkata
• Rakesh Kumar, Indian Statistical Institute, Kolkata
• Subhamoy Maitra, Indian Statistical Institute, Kolkata

Article Type

Research Article

Publication Title

International Journal of Theoretical Physics

Abstract

Mutually Unbiased Bases (MUBs) are closely connected with quantum physics and the structure has a rich mathematical background. We provide equivalent criteria for extending a set of MUBs for by studying real points of a certain affine algebraic variety. This variety comes from the relations that determine the extendability of a system of MUBs. Finally, we show that some part of this variety gives rise to complete intersection domains. Further, we show that there is a one-to-one correspondence between MUBs and the maximal commuting classes (bases) of orthogonal normal matrices in. It means that for m MUBs in, there are m commuting classes each consisting n commuting orthogonal normal matrices and the existence of maximal commuting basis for ensures the complete set of MUBs in.

DOI

10.1007/s10773-025-06094-3

Publication Date

9-1-2025

Recommended Citation

Banerjee, Arindam; Das, Kanoy Kumar; Kumar, Ajeet; Kumar, Rakesh; and Maitra, Subhamoy, "On Obtaining New MUBs by Finding Points on Complete Intersection Varieties over" (2025). Journal Articles. 5492.
https://digitalcommons.isical.ac.in/journal-articles/5492