**The Problem of Finding A Maximal Set of MUBs When d = 6**

The smallest dimension that is not an integer power of a prime is *d* = 6. This is also the smallest dimension for which the number of mutually unbiased bases is not known. The methods used to determine the number of mutually unbiased bases when *d* is an integer power of a prime number cannot be used in this case. Searches for a set of four mutually unbiased bases when *d* = 6, both by using Hadamard matrices and numerical methods have been unsuccessful. The general belief is that the maximum number of mutually unbiased bases for *d* = 6 is .

Read more about this topic: Mutually Unbiased Bases

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