Nullifier Variance Analyzer

Calculate nullifier variances ⟨δ²⟩ as entanglement witnesses through covariance matrix propagation

Nullifier Variance Computation

The nullifier variance is computed from the covariance matrix V and the nullifier coefficient vector c:

⟨δj²⟩ = cT V c

where c = (0,...,-Aj1,...,0,1,0,...,-AjN,...)

Entanglement Criterion:

  • ⟨δ²⟩ < 1 SNU: Genuine entanglement
  • ⟨δ²⟩ ≈ 1 SNU: Marginal / threshold
  • ⟨δ²⟩ > 1 SNU: No entanglement witness

SNU = Symmetrized Natural Units (shot noise = 1)

Graph Configuration

Mesh Configuration

Analysis Results

Average Nullifier Variance
0.250 SNU
Maximum Variance
0.312 SNU
Minimum Variance
0.188 SNU
Entangled Modes
7/7
Entanglement Status
ENTANGLED

Mode-wise Nullifier Variances

Variance vs Input Squeezing

Output Covariance Matrix