An application of the measurement of expectation values for the photon annihilation and creation operators. (arXiv:1709.01697v3 [quant-ph] UPDATED)

Motivated by the readout scheme in interferometric gravitational-wave
detectors, we consider the device which measures the expectation value of the
photon annihilation and creation operators for output optical field from the
main interferometer. As the result, the eight-port homodyne detection is
rediscovered as such a device. We evaluate the noise spectral density in this
measurement. We also briefly discuss on the application of our results to the
readout scheme of gravitational-wave detectors. We call this measurement scheme
to measure these expectation values as "double balanced homodyne detection."

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