  The eight-port homodyne detection apparatus is analyzed in the framework of
the operational theory of quantum measurement. For an arbitrary quantum noise
leaking through the unused port of the beam splitter, the positive operator
valued measure and the corresponding operational homodyne observables are
derived. It is shown that such an eight-port homodyne device can be used to
construct the operational quantum trigonometry of an optical field. The quantum
trigonometry and the corresponding phase space Wigner functions are derived for
a signal field probed by a classical local oscillator and a squeezed vacuum in
the unused port.
