Quantum Amplifier Noise: Phase-Insensitive vs Phase-Sensitive

Amplifier mode

Both quadratures amplified equally — quantum mechanics forbids zero added noise here.

Gain

Power gain G 4.0×

Signal phase

Quadrature angle θ_s 0°

0° = amplifier's favored (amplified) axis. 90° = the perpendicular (squeezed) axis.

Output noise (this quadrature)

Variance (shot-noise units)

–

Effective gain g(θ_s)

–

Noise figure at θ_s

–

SQL floor (phase-ins.)

3.0 dB

Legend

Input (vacuum-limited) Output — phase-insensitive Output — phase-sensitive

Why is there a floor at all?

Any amplifier that treats both quadratures (X₁, X₂) the same way must, by the Heisenberg uncertainty relation, add at least (G−1) units of vacuum noise per quadrature — a hard floor of ≈3 dB of noise figure as G grows, no matter how the device is engineered.

A phase-sensitive (degenerate parametric) amplifier sidesteps this by amplifying one quadrature and de-amplifying (squeezing) the other. It can add essentially zero noise to the favored quadrature — but only that one. Any information riding on the perpendicular quadrature is squeezed down and, once any realistic downstream noise is added, becomes far noisier than the phase-insensitive floor.

Phase-insensitive

Noise figure vs quadrature angleG = 4.0×

Dashed line: phase-insensitive floor (flat — never beaten, at any angle or gain). Solid curve: phase-sensitive noise figure, which dips below the floor near the amplified axis and rises above it near the squeezed axis, once a realistic downstream noise floor (1 shot-noise unit) is included.