Abstract:Constructing four six-dimensional mutually unbiased bases (MUBs) is an open problem in quantum physics and measurement. We investigate the existence of four MUBs including the identity, and a complex Hadamard matrix (CHM) of Schmidt rank three. The CHM is equivalent to a controlled unitary operation on the qubit-qutrit system via local unitary transformation I2 ⊗ V and I2 ⊗ W . We show that V and W have no zero entry, and apply it to exclude examples as members of MUBs. We further show that the maximum of ent… Show more
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