Department of Mathematical Sciences
QIT Thinking Seminar
Wednesday, February 4th, 2026
4:00PM-4:50PM
Stratton Hall 311
Speaker: Bill Martin, WPI
Title: Mutually unbiased bases
Abstract: This talk will introduce the main problem related to the construction of mutually unbiased bases (“MUBs”) in Cd, d-dimensional complex space.
Mutually unbiased bases, introduced by Schwinger in 1960 and can (hypothetically, at least) be used in quantum state tomography and quantum cryptography. Given a pair of unitary bases for Cd, the first is “unbiased” with respect to the second if the measurement of any vector in the first basis using the second basis yields a uniform distribution on the d outcomes. We say a set of k bases is a set of k MUBs if any one is unbiased with respect to any other. The maximum size of a set of MUBs in dimension d is k ≤ d+1. After decades of progress, we still cannot construct configurations reaching this bound in any dimension that is not a prime power. The main problem is to find, for each dimension d, the maximum number k of mutually unbiased bases in complex dimension d.
In this talk, I will discuss a construction due to Bill Kantor using bent functions (maximally non-linear functions) and a possible extension of this technique to other dimensions. As time permits, I will discuss the real case and/or applications and related problems.