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A Hermitian Opetator Conjugate to Two-Mode Number-Difference Operator

For the Shapiro-Wagner-Hradil phase detection description the canonical commutation relation between phase angle ψ and two-mode number-difference operator D = a† a - b† b is constructed. Departing from [ψ, D] = -i, the phase angle Hermitian operator is derived in the newly obtained representation ⟨ξ|, where|ξ⟩ is the common eigenket of a + b† and b + a†.