On balanced homodyne measurement -- simple proof of wave function collapse

TL;DR

The paper provides a simple proof that balanced homodyne detection measures the quadrature phase amplitude, showing how the wave function collapses to an eigenstate after measurement, using elementary calculus.

Contribution

It offers an elementary calculus-based proof of wave function collapse in balanced homodyne measurement, clarifying the measurement process in quantum optics.

Findings

Balanced homodyne detector measures quadrature phase amplitude.

Wave function collapses to eigenstate after measurement.

Proof uses elementary calculus for clarity.

Abstract

Using only elementary calculus we prove that the balanced homodyne detector measures the quadrature phase amplitude of a signal. More precisely, after the measurement of photon numbers $l$, the collapse of the composite state of a strong laser beam and a signal approximates the collapse of the signal to the eigen-state of quadrature phase amplitude with eigen-value $r$.