qfi-entanglement-robustness - SKILL.md Agent Skill

name: "qfi-entanglement-robustness" description: "Information-geometric framework for analyzing entanglement robustness using quantum Fisher information (QFI). Establishes bounds on concurrence reduction caused by parameter uncertainty in entanglement generation. Use when analyzing quantum entanglement stability, quantum network reliability, quantum sensing precision, or parameter-dependent quantum operations. Activation: quantum Fisher information, entanglement robustness, concurrence bounds, quantum network reliability, quantum sensing precision, parameter uncertainty"

QFI-Based Entanglement Robustness Analysis

Information-geometric bounds on entanglement generation robustness. Based on arXiv:2606.05696 (Saleem, 2026).

Core Result

For two interacting qubits, the reduction in concurrence caused by fluctuations in the interaction parameter θ is bounded by the quantum Fisher information (QFI) with respect to θ:

ΔC ≤ √(F_Q(θ)) · δθ

where:

C = concurrence (entanglement measure)
F_Q(θ) = quantum Fisher information w.r.t. interaction parameter
δθ = parameter uncertainty/fluctuation magnitude

Key Insight

QFI — traditionally used for parameter estimation precision — directly bounds entanglement degradation. This connects quantum metrology with quantum information processing reliability.

Application Patterns

1. Quantum Network Reliability Assessment

When designing quantum repeaters or network nodes:

Compute QFI for the entangling gate parameter
Measure expected parameter fluctuations (calibration drift, thermal noise)
Bound worst-case concurrence loss
If bound exceeds acceptable threshold → improve calibration or use error mitigation

2. Quantum Sensing-Entanglement Trade-off

High QFI means:

✅ Better parameter estimation precision (good for sensing)
⚠️ Higher sensitivity to parameter fluctuations (bad for entanglement stability)

Design implication: optimize for the actual use case. Sensing benefits from high QFI; entanglement distribution may benefit from parameter-insensitive interactions.

3. Entanglement Generation Protocol Design

Step 1: Characterize interaction Hamiltonian H(θ)
Step 2: Compute QFI = 4·(⟨∂θψ|∂θψ⟩ - |⟨ψ|∂θψ⟩|²)
Step 3: Estimate parameter variance σ²_θ from hardware specs
Step 4: Bound concurrence loss: ΔC ≤ 2·√(F_Q)·σ_θ
Step 5: If ΔC > tolerance → modify protocol or add error correction

Computational Recipe

QFI for Pure States

import numpy as np

def qfi_pure_state(psi, d_psi_dtheta):
    """Compute QFI for a pure state |ψ(θ)⟩."""
    # F_Q = 4[⟨∂θψ|∂θψ⟩ - |⟨ψ|∂θψ⟩|²]
    term1 = np.vdot(d_psi_dtheta, d_psi_dtheta).real
    term2 = np.abs(np.vdot(psi, d_psi_dtheta))**2
    return 4 * (term1 - term2)

QFI for Mixed States (via SLD)

from scipy.linalg import eig

def qfi_mixed_state(rho, d_rho_dtheta):
    """Compute QFI for mixed state via symmetric logarithmic derivative."""
    # Solve: dρ/dθ = (L·ρ + ρ·L)/2 for L
    # Then F_Q = Tr(ρ·L²)
    evals, evecs = eig(rho)
    n = len(evals)
    L = np.zeros((n, n), dtype=complex)
    for i in range(n):
        for j in range(n):
            if evals[i] + evals[j] > 1e-12:
                L[i,j] = 2 * np.vdot(evecs[:,i], d_rho_dtheta @ evecs[:,j]) / (evals[i] + evals[j])
    L = evecs @ L @ evecs.conj().T
    return np.real(np.trace(rho @ L @ L))

Related Work

arXiv:2605.31525 — Seedless extractors for device-independent QKD (complementary DI approach)
arXiv:2605.29694 — Tripartite interactions for correlated quantum emissions
arXiv:2605.30005 — Diamond color defects for quantum networks

Activation Keywords

quantum Fisher information, QFI bounds, entanglement robustness
concurrence degradation, parameter uncertainty, quantum network reliability
quantum sensing precision, entanglement stability