While there has been investigation into mutually unbiased bases in infinite dimension Hilbert space, their existence remains an open question. It is conjectured that in a continuous Hilbert space, two orthonormal bases | ψ ψ s b ⟩ ⟩ and | ψ ψ s ′ b ′ ⟩ ⟩ are said to be mutually unbiased if