quantum-dephasing-dynamics

name	quantum-dephasing-dynamics
description	Analysis of dephasing effects on quantum correlations and coherence dynamics in oscillating quantum systems. Covers quantum steering, logarithmic negativity, and coherence measures under environmental decoherence. Use when analyzing quantum system robustness to noise, studying decoherence in quantum oscillators/neutrino systems, or evaluating quantum resource preservation.

Quantum Dephasing Dynamics

Methodology from Bachain, Jaloum & Amazioug (2026) "Dephasing Effects on the Dynamical Evolution of Quantum Correlations and Coherence in Neutrino Oscillations" (arXiv:2605.05015).

Core Framework

Analyze quantum resource dynamics under dephasing using three complementary measures:

1. Quantum Steering

• Quantifies the ability of one subsystem to remotely prepare states of another
• More robust than entanglement under certain noise conditions
• Directional: A→B steering ≠ B→A steering

2. Logarithmic Negativity

• Entanglement monotone for mixed states
• Computed from partial transpose of density matrix
• N(ρ) = log₂||ρ^{T_A}||₁

3. l₁-Norm Coherence

• Sum of absolute values of off-diagonal density matrix elements
• C_{l₁}(ρ) = Σ_{i≠j} |ρ_{ij}|
• Measures superposition strength in a reference basis

Dephasing Model

Dephasing destroys off-diagonal elements of the density matrix:

ρ(t) = Σ_{ij} ρ_{ij}(0) · e^{-γ_{ij}·t} · |i⟩⟨j|

where γ_{ij} is the dephasing rate between states |i⟩ and |j⟩.

Analysis Pipeline

def analyze_quantum_dephasing(rho_0, hamiltonian, dephasing_rates, time_points):
    """
    Analyze quantum resource evolution under dephasing.
    
    Returns:
        Dict with steering, negativity, coherence vs time
    """
    results = {
        'steering_AB': [],
        'steering_BA': [],
        'negativity': [],
        'coherence_l1': [],
        'time': time_points
    }
    
    for t in time_points:
        # 1. Evolve density matrix under dephasing
        rho_t = evolve_dephasing(rho_0, hamiltonian, dephasing_rates, t)
        
        # 2. Compute quantum resources
        results['steering_AB'].compute_steering(rho_t, direction='AB')
        results['steering_BA'].compute_steering(rho_t, direction='BA')
        results['negativity'].compute_negativity(rho_t)
        results['coherence_l1'].compute_l1_coherence(rho_t)
    
    return results

Key Findings

1. Steering sudden death: Quantum steering can vanish at finite time
2. Negativity decay rate: Depends on initial state structure
3. Coherence hierarchy: Different coherence measures decay at different rates
4. Oscillation modulation: System dynamics modulate dephasing effects

When to Use

Scenario	Recommended Analysis
Quantum communication channel	Steering + coherence
Quantum computation robustness	Negativity + coherence
Sensor noise characterization	All three measures
State preparation quality	Coherence l₁-norm

Pitfalls

• Steering criteria are sufficient but not necessary conditions
• l₁-coherence is basis-dependent
• Dephasing model assumes Markovian environment
• Non-Markovian effects can cause coherence revival

Activation Keywords

• quantum dephasing, decoherence analysis
• quantum steering, logarithmic negativity
• coherence measures, quantum resources
• quantum noise, oscillator decoherence