Quantum Fisher Information & Cramér-Rao Bound

The QFI F_Q(ρ,H) sets the fundamental precision limit for parameter estimation: Var(θ̂) ≥ 1/F_Q. For pure states F_Q = 4ΔH². Entangled probes beat the SQL (1/N) and approach the Heisenberg limit (1/N²).

N probes N = 10 Entanglement (GHZ frac) ξ = 0.00 Noise (dephasing γ) γ = 0.00

SQL: Var ≥ 1/N | HL: Var ≥ 1/N² | QFI_sep = N | QFI_GHZ = N²