Mutually Unbiased Bases (MUBs)

Complex vector spaces are interesting not only mathematically but also physically since quantum mechanics can be formulated conveniently in terms of vectors with complex components. Two bases are called mutually unbiased if the square of the magnitude of the inner product between any basis vectors (each belonging to different bases) equals the inverse of the dimension. It is an open question how many MUBs can be found in arbitrary dimension. The maximum number of MUBs is known when dimension is an integer power of a prime number. The smallest dimension that is not an integer power of a prime is six. The aim of this project is to examine low dimensional known solutions and to gain insight about the open problem of six dimensions. Connection with the number of mutually orthogonal Latin squares (MOLS) will also be studied.