Manuscript Em03-D@1 · Em03-D-v1.tex · proposition · 450d878a

Proposition: Required conjugate noise growth

Probe preparation, noise, and squeezing cost › A numerical form of the noise bound · lines 1515–1532 · proof included or linked

Em03-D@1#prop:effort

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The conjugate probe quadrature obeys

V_{σ_{R, ϵ}} (p_{ϵ}, p_{ϵ}) \geq \frac{1}{4 N _{R} ϵ ^{2}} .

The squeezing parameter has magnitude $2 lo g (1/ ϵ)$ , and the processing test is $g / ϵ$ .

Proof. The two quadratures have commutator $i I$ . The uncertainty inequality gives the variance product at least $1/4$ . Apply (eq:noisebound). The remaining assertions are the two scalings in (eq:squeeze) and (eq:probeeffect).

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unlabeled · line 1518
$V_{σ_{R, ϵ}} (p_{ϵ}, p_{ϵ}) \geq \frac{1}{4 N _{R} ϵ ^{2}} .$

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section: A numerical form of the noise bound
section: A numerical form of the noise bound