Minimum Uncertainty States for Number-Difference-Phase Uncertainty Relation in NFM Operational Phase Description

For the Noh, Fougères and Mandel (NFM) operational quantum phase description, which is based on an eight-port homodyne-detection, we derive the minimum uncertainty states for the number-difference-phase uncertainty relation. The derivation makes full use of the newly constructed |q,r> representation which is the common eigenvector of the two-mode photon number-difference a^†a - b^†b and (a+b^†)(a^†+ b).