A pair of orthonormal bases of the d-dimensional complex space are mutually unbiased if the square of their standard hermitian inner product is equal to 1/d. We briefly motivate why this notion of mutually unbiased bases (MUBs) is of great importance in quantum information theory, then discuss the existing mathematical tools and difficulties in constructing MUBs, including the relationship to orthogonal pairs of special linear Lie algebras.
Mutually Unbiased Bases and Lie Algebras
Oct. 19, 2022 4:40pm (MATH 3…
Grad Student Seminar
Adrian Neff (CU Boulder)
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Michael Artin supposedly said that you can understand most concepts in moduli through the moduli space of triangles (source: someone told me this once). With this advice in mind, this talk will do just that: we will go through multiple variations on the moduli space of triangles in order to see various behaviors of moduli problems, and hopefully by the end (unless Artin was a liar), we will all understand moduli spaces.