TL;DR
This paper explores the mathematical classification of complex Hadamard matrices and their relation to quantum state space geometry, highlighting the influence of prime number decomposition on quantum complementarity.
Contribution
It links the classification of complex Hadamard matrices to the prime decomposition of Hilbert space dimensions, advancing understanding of quantum complementarity.
Findings
Complementarity depends on prime decomposition of Hilbert space dimensions.
Classification of complex Hadamard matrices is crucial for understanding quantum bases.
Quantum state space geometry is influenced by the structure of Hadamard matrices.
Abstract
Bohr placed complementary bases at the mathematical centre point of his view of quantum mechanics. On the technical side then my question translates into that of classifying complex Hadamard matrices. Recent work (with Barros e Sa) shows that the answer depends heavily on the prime number decomposition of the Hilbert space. By implication so does the geometry of quantum state space.
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.