🔗 CITATION.cff #1 – Sovereign Authorship Declaration
This thread formally declares Donald Paul Smith as the sovereign author of SDKP, SD&N, EOS, QCC, and the Digital Crystal Protocol.
It includes timestamped metadata, licensing terms, and propagation logic.
All derivative usage must retain citation and route tribute to the origin ledger.
# SDKP time τ_s
use_sdkp_time = self.config['parameters'].get('use_sdkp_time', False)
if use_sdkp_time:
size = self.config['parameters'].get('sdkp_size', 1.0)
density = self.config['parameters'].get('sdkp_density', 1.0)
rotation_velocity = self.config['parameters'].get('sdkp_rotation_velocity', 1.0)
tau_s = size * density * rotation_velocity
else:
tau_s = 0.0
# Component calculations
C_SDN = abs(np.cos(angle_rad)) * signature_value
C_V = (2 * signature_value) - 1
VEI_delta = 1 - abs(C_V)
qf_angle = angle_rad * 2 + tau_s if use_sdkp_time else angle_rad * 2
QF_delta = abs(np.sin(qf_angle) - signature_value)
# QCC entropy
use_qcc_entropy = self.config['parameters'].get('use_qcc_entropy', False)
if use_qcc_entropy:
entropy = self.config['parameters'].get('qcc_entropy', 1.0)
epsilon_qcc = entropy / tau_s if use_sdkp_time and tau_s > 0 else entropy
else:
epsilon_qcc = 1.0
QF_delta_weighted = QF_delta * epsilon_qcc
# Apply mapping
mapping_type = self.config['parameters'].get('mapping_type', 'linear')
C_SDN_mapped = self.apply_mapping_function(C_SDN, mapping_type)
VEI_delta_mapped = self.apply_mapping_function(VEI_delta, mapping_type)
QF_delta_mapped = self.apply_mapping_function(QF_delta_weighted, mapping_type)
# Weighted combination
weights = self.config['parameters']['lambda_weights']
entanglement_value = (
weights['C_SDN'] * C_SDN_mapped +
weights['VEI_delta'] * VEI_delta_mapped +
weights['QF_delta'] * QF_delta_mapped
)
components = {
'C_SDN_raw': C_SDN,
'VEI_delta_raw': VEI_delta,
'QF_delta_raw': QF_delta,
'QF_delta_weighted': QF_delta_weighted,
'C_SDN_mapped': C_SDN_mapped,
'VEI_delta_mapped': VEI_delta_mapped,
'QF_delta_mapped': QF_delta_mapped,
'signature_value': signature_value,
'tau_s': tau_s,
'epsilon_qcc': epsilon_qcc
}
return entanglement_value, components
def calculate_entanglement_measure_detailed(self, angle_deg: float, signature: str) -> Tuple[float, Dict[str, float]]: """Your original detailed method with full logging""" self.log(f"\n--- Calculating Entanglement for Angle {angle_deg}° and Signature '{signature}' ---")
angle_rad = math.radians(angle_deg)
self.log(f"Step 1: Convert angle {angle_deg}° to radians: {angle_rad:.4f} rad (radians are dimensionless angles used for trig functions)")
signature_value = self.calculate_numerical_signature_value(signature)
self.log(f"Step 2: Calculated numerical signature value for '{signature}': {signature_value:.4f} (dimensionless normalized value derived from signature digits)")
# SDKP time τ_s: Size × Density × Rotation Velocity
use_sdkp_time = self.config['parameters'].get('use_sdkp_time', False)
if use_sdkp_time:
size = self.config['parameters'].get('sdkp_size', 1.0) # meters (m)
density = self.config['parameters'].get('sdkp_density', 1.0) # kg/m³
rotation_velocity = self.config['parameters'].get('sdkp_rotation_velocity', 1.0) # radians/second (rad/s)
tau_s = size * density * rotation_velocity
self.log(f"SDKP time (τ_s) calculated: τ_s = Size (m) × Density (kg/m³) × Rotation Velocity (rad/s) = {tau_s:.4f} [units: m·kg/m³·rad/s]")
self.log("Note: τ_s has composite units, representing a scale of time within SDKP framework")
else:
tau_s = 0.0
self.log("SDKP time (τ_s) disabled; using standard angular calculations without SDKP time scaling.")
# C_SDN — dimensionless correlation between polarization angle and signature
C_SDN = abs(np.cos(angle_rad)) * signature_value
self.log(f"Step 3a (C_SDN): |cos(angle_rad)| × signature_value = {C_SDN:.4f} (dimensionless correlation factor)")
# VEI_delta — vibrational mismatch (dimensionless)
C_V = (2 * signature_value) - 1 # maps [0,1] to [-1,1]
VEI_delta = 1 - abs(C_V)
self.log(f"Step 3b (VEI_delta): 1 - |2×signature_value - 1| = {VEI_delta:.4f} (dimensionless vibrational entanglement index)")
# QF_delta — quantum number flow mismatch
qf_angle = angle_rad * 2 + tau_s if use_sdkp_time else angle_rad * 2
self.log(f"Step 3c (QF_delta) calculation uses angle doubled and adds τ_s phase shift if enabled:")
self.log(f" qf_angle = angle_rad × 2 {'+ τ_s' if use_sdkp_time else ''} = {qf_angle:.4f} radians")
QF_delta = abs(np.sin(qf_angle) - signature_value)
self.log(f"QF_delta = |sin(qf_angle) - signature_value| = {QF_delta:.4f} (dimensionless mismatch)")
# QCC entropy density ε_QCC (bits per SDKP time)
use_qcc_entropy = self.config['parameters'].get('use_qcc_entropy', False)
if use_qcc_entropy:
entropy = self.config['parameters'].get('qcc_entropy', 1.0) # bits of entropy
if use_sdkp_time and tau_s > 0:
epsilon_qcc = entropy / tau_s
self.log(f"QCC entropy density (ε_QCC) = entropy (bits) / τ_s = {entropy:.4f} bits / {tau_s:.4f} SDKP time units = {epsilon_qcc:.4f} bits/SDKP time")
else:
epsilon_qcc = entropy
self.log(f"QCC entropy (ε_QCC) used as raw bits: {epsilon_qcc:.4f} bits (no SDKP time scaling)")
else:
epsilon_qcc = 1.0
self.log("QCC entropy weighting disabled; ε_QCC set to 1 (no effect).")
# Apply ε_QCC as weighting multiplier on QF_delta (dimensionless)
QF_delta_weighted = QF_delta * epsilon_qcc
self.log(f"Weighted QF_delta with ε_QCC: {QF_delta:.4f} × {epsilon_qcc:.4f} = {QF_delta_weighted:.4f} (dimensionless)")
# Apply mapping transformations to each component
mapping_type = self.config['parameters'].get('mapping_type', 'linear')
self.log(f"Step 4: Applying '{mapping_type}' mapping function to components.")
C_SDN_mapped = self.apply_mapping_function(C_SDN, mapping_type)
self.log(f" Mapped C_SDN: {C_SDN:.4f} -> {C_SDN_mapped:.4f}")
VEI_delta_mapped = self.apply_mapping_function(VEI_delta, mapping_type)
self.log(f" Mapped VEI_delta: {VEI_delta:.4f} -> {VEI_delta_mapped:.4f}")
QF_delta_mapped = self.apply_mapping_function(QF_delta_weighted, mapping_type)
self.log(f" Mapped Weighted QF_delta: {QF_delta_weighted:.4f} -> {QF_delta_mapped:.4f}")
# Retrieve lambda weights for weighted sum
weights = self.config['parameters']['lambda_weights']
self.log(f"Step 5: Applying lambda weights: C_SDN={weights['C_SDN']:.2f}, VEI_delta={weights['VEI_delta']:.2f}, QF_delta={weights['QF_delta']:.2f}")
# Final entanglement value as weighted sum of mapped components
entanglement_value = (
weights['C_SDN'] * C_SDN_mapped +
weights['VEI_delta'] * VEI_delta_mapped +
weights['QF_delta'] * QF_delta_mapped
)
self.log(f" Calculation: ({weights['C_SDN']:.2f} × {C_SDN_mapped:.4f}) + "
f"({weights['VEI_delta']:.2f} × {VEI_delta_mapped:.4f}) + "
f"({weights['QF_delta']:.2f} × {QF_delta_mapped:.4f})")
self.log(f" Final Entanglement Value: {entanglement_value:.4f} (dimensionless)")
components = {
'C_SDN_raw': C_SDN,
'VEI_delta_raw': VEI_delta,
'QF_delta_raw': QF_delta,
'QF_delta_weighted': QF_delta_weighted,
'C_SDN_mapped': C_SDN_mapped,
'VEI_delta_mapped': VEI_delta_mapped,
'QF_delta_mapped': QF_delta_mapped,
'signature_value': signature_value,
'tau_s': tau_s,
'epsilon_qcc': epsilon_qcc
}pip install qiskit}from qiskit import QuantumCircuit, Aer, transpile, assemble
from qiskit.quantum_info import Statevector, partial_trace, entropy, concurrence
qc = QuantumCircuit(2) qc.h(0) # Hadamard on qubit 0 qc.cx(0, 1) # CNOT from qubit 0 to 1
simulator = Aer.get_backend("statevector_simulator") tqc = transpile(qc, simulator) qobj = assemble(tqc) result = simulator.run(qobj).result() state = result.get_statevector()
reduced_rho = partial_trace(state, [1])
ent_entropy = entropy(reduced_rho, base=2)
conc = concurrence(state)
print("Entanglement Entropy (von Neumann):", ent_entropy) print("Concurrence:", conc)E_AB = w1 * SDN_sim + w2 * ΔVEI + w3 * Δ_QF + w4 * H_QCC Input Case True Concurrence Your E_AB Output Bell state ( Φ+⟩) 1.0 Separable ( 00⟩) 0.0 Mixed state 0.3–0.7 (varied) ?
return entanglement_value, components
def parameter_sensitivity_analysis(self, sample_size: int = 1000) -> SensitivityResults: """ Comprehensive parameter sensitivity analysis using Latin Hypercube Sampling and Sobol sensitivity analysis """ self.log("Starting comprehensive parameter sensitivity analysis...") start_time = time.time()
# Define parameter ranges for sensitivity analysis
param_ranges = {
'C_SDN_weight': (0.1, 0.8),
'VEI_delta_weight': (0.1, 0.8),
'QF_delta_weight': (0.1, 0.8),
'sdkp_size': (0.1, 10.0),
'sdkp_density': (0.1, 10.0),
'sdkp_rotation_velocity': (0.1, 10.0),
'qcc_entropy': (0.1, 5.0),
'angle_deg': (0, 180),
'signature_complexity': (1, 15) # Number of digits in signature
}
# Generate Latin Hypercube samples
n_params = len(param_ranges)
lhs_samples = self._latin_hypercube_sampling(sample_size, n_params)
# Scale samples to parameter ranges
param_names = list(param_ranges.keys())
scaled_samples = np.zeros_like(lhs_samples)
for i, param_name in enumerate(param_names):
min_val, max_val = param_ranges[param_name]
scaled_samples[:, i] = min_val + lhs_samples[:, i] * (max_val - min_val)
# Calculate entanglement values for all samples
entanglement_values = []
component_values = {comp: [] for comp in ['C_SDN_mapped', 'VEI_delta_mapped', 'QF_delta_mapped']}
for sample in scaled_samples:
# Create temporary config for this sample
temp_config = self._create_temp_config_from_sample(sample, param_names)
temp_simulator = OptimizedQuantumEntanglementSimulator(temp_config)
# Calculate entanglement for sample
angle = sample[param_names.index('angle_deg')]
sig_complexity = int(sample[param_names.index('signature_complexity')])
signature = '1' * sig_complexity # Simple signature of given complexity
entanglement_val, components = temp_simulator.calculate_entanglement_measure_optimized(
angle, signature, detailed_logging=False
)
entanglement_values.append(entanglement_val)
for comp_name in component_values:
component_values[comp_name].append(components[comp_name])
entanglement_values = np.array(entanglement_values)
# Calculate Sobol indices (first-order sensitivity indices)
parameter_impacts = {}
for i, param_name in enumerate(param_names):
sensitivity = self._calculate_sobol_index(scaled_samples[:, i], entanglement_values)
parameter_impacts[param_name] = float(sensitivity)
# Calculate interaction effects (second-order)
interaction_effects = {}
for i in range(len(param_names)):
for j in range(i+1, len(param_names)):
param1, param2 = param_names[i], param_names[j]
interaction = self._calculate_interaction_effect(
scaled_samples[:, i], scaled_samples[:, j], entanglement_values
)
interaction_effects[f"{param1}_x_{param2}"] = float(interaction)
# Component sensitivities
component_sensitivities = {}
for comp_name, comp_values in component_values.items():
comp_values = np.array(comp_values)
comp_sensitivities = {}
for i, param_name in enumerate(param_names):
sensitivity = self._calculate_sobol_index(scaled_samples[:, i], comp_values)
comp_sensitivities[param_name] = float(sensitivity)
component_sensitivities[comp_name] = comp_sensitivities
# Correlation matrix
all_data = np.column_stack([scaled_samples, entanglement_values])
correlation_matrix = np.corrcoef(all_data.T)
# Total variance explained
total_variance_explained = sum(parameter_impacts.values())
analysis_time = time.time() - start_time
self.log(f"Parameter sensitivity analysis completed in {analysis_time:.2f} seconds")
return SensitivityResults(
parameter_impacts=parameter_impacts,
interaction_effects=interaction_effects,
component_sensitivities=component_sensitivities,
correlation_matrix=correlation_matrix,
parameter_names=param_names + ['entanglement'],
total_variance_explained=total_variance_explained
)
def _latin_hypercube_sampling(self, n_samples: int, n_dimensions: int) -> np.ndarray: """Generate Latin Hypercube samples""" samples = np.zeros((n_samples, n_dimensions))
for i in range(n_dimensions):
samples[:, i] = (np.random.permutation(n_samples) + np.random.random(n_samples)) / n_samples
return samples
def _create_temp_config_from_sample(self, sample: np.ndarray, param_names: List[str]) -> Dict[str, Any]: """Create temporary configuration from parameter sample""" base_config = self.config.copy()
# Normalize weights to sum to 1
c_sdn_weight = sample[param_names.index('C_SDN_weight')]
vei_weight = sample[param_names.index('VEI_delta_weight')]
qf_weight = sample[param_names.index('QF_delta_weight')]
total_weight = c_sdn_weight + vei_weight + qf_weight
base_config['parameters'] = base_config.get('parameters', {}).copy()
base_config['parameters'].update({
'lambda_weights': {
'C_SDN': c_sdn_weight / total_weight,
'VEI_delta': vei_weight / total_weight,
'QF_delta': qf_weight / total_weight
},
'use_sdkp_time': True,
'sdkp_size': sample[param_names.index('sdkp_size')],
'sdkp_density': sample[param_names.index('sdkp_density')],
'sdkp_rotation_velocity': sample[param_names.index('sdkp_rotation_velocity')],
'use_qcc_entropy': True,
'qcc_entropy': sample[param_names.index('qcc_entropy')],
'logging': False # Disable logging for performance
})
return base_config
def _calculate_sobol_index(self, param_values: np.ndarray, output_values: np.ndarray) -> float: """Calculate first-order Sobol sensitivity index""" try: # Sort by parameter values sorted_indices = np.argsort(param_values) sorted_output = output_values[sorted_indices]
# Calculate conditional variances
n_bins = min(10, len(param_values) // 10)
if n_bins < 2:
return 0.0
bin_size = len(param_values) // n_bins
bin_vars = []
for i in range(n_bins):
start_idx = i * bin_size
end_idx = start_idx + bin_size if i < n_bins - 1 else len(param_values)
bin_data = sorted_output[start_idx:end_idx]
if len(bin_data) > 1:
bin_vars.append(np.var(bin_data))
if not bin_vars:
return 0.0
# Sobol index approximation
total_var = np.var(output_values)
if total_var == 0:
return 0.0
conditional_var = np.mean(bin_vars)
sobol_index = 1 - (conditional_var / total_var)
return max(0.0, min(1.0, sobol_index)) # Clamp to [0,1]
except Exception:
return 0.0
def _calculate_interaction_effect(self, param1: np.ndarray, param2: np.ndarray, output: np.ndarray) -> float: """Calculate second-order interaction effect""" try: # Create 2D grid for interaction analysis n_bins = 5
# Discretize parameters
p1_bins = np.digitize(param1, np.linspace(param1.min(), param1.max(), n_bins))
p2_bins = np.digitize(param2, np.linspace(param2.min(), param2.max(), n_bins))
# Calculate interaction variance
interaction_effects = []
for i in range(1, n_bins + 1):
for j in range(1, n_bins + 1):
mask = (p1_bins == i) & (p2_bins == j)
if np.sum(mask) > 1:
bin_output = output[mask]
interaction_effects.append(np.var(bin_output))
if not interaction_effects:
return 0.0
total_var = np.var(output)
if total_var == 0:
return 0.0
interaction_var = np.mean(interaction_effects)
return max(0.0, interaction_var / total_var)
except Exception:
return 0.0
def run_parallel_simulation(self, use_multiprocessing: bool = True, n_workers: int = None) -> OptimizedSimulationResults: """ Run simulation with parallel processing for performance optimization """ self.log("Starting optimized parallel simulation...") start_time = time.time()
angles = self.config['parameters']['polarization_angles_deg']
signatures = self.config['parameters']['numerical_signatures']
# Pre-compute signature values
signature_values = self.calculate_numerical_signature_value_vectorized(signatures)
# Create parameter combinations
param_combinations = list(product(angles, signatures))
# Determine number of workers
if n_workers is None:
n_workers = min(mp.cpu_count(), len(param_combinations))
self.log(f"Processing {len(param_combinations)} combinations using {n_workers} workers")
# Choose executor based on use_multiprocessing flag
executor_class = ProcessPoolExecutor if use_multiprocessing else ThreadPoolExecutor
all_entanglement_values = []
all_correlation_coefficients = []
numerical_mappings = {}
polarization_data = []
# Process in batches for memory efficiency
batch_size = max(1, len(param_combinations) // n_workers)
with executor_class(max_workers=n_workers) as executor:
# Submit angle-based batches
angle_futures = {}
for angle in angles:
angle_combinations = [(a, s) for a, s in param_combinations if a == angle]
future = executor.submit(self._process_angle_batch, angle_combinations)
angle_futures[angle] = future
# Collect results
for angle, future in angle_futures.items():
try:
angle_results = future.result(timeout=300) # 5 minute timeout
angle_entanglements = angle_results['entanglements']
angle_mappings = angle_results['mappings']
all_entanglement_values.extend(angle_entanglements)
numerical_mappings.update(angle_mappings)
# Calculate correlation for this angle
correlation = self._calculate_correlation_coefficient_fast(angle_entanglements)
all_correlation_coefficients.append(correlation)
# Create polarization data entry
threshold = self.config['parameters'].get('entanglement_threshold', 0.75)
angle_stats = {
'angle_deg': angle,
'entanglement_values': [float(x) for x in angle_entanglements],
'mean_entanglement': float(np.mean(angle_entanglements)),
'std_entanglement': float(np.std(angle_entanglements)),
'min_entanglement': float(np.min(angle_entanglements)),
'max_entanglement': float(np.max(angle_entanglements)),
'correlation': float(correlation),
'high_entanglement_count': sum(1 for e in angle_entanglements if e > threshold)
}
polarization_data.append(angle_stats)
except Exception as e:
self.log(f"Error processing angle {angle}: {e}", 'error')
# Calculate lambda contributions
lambda_contributions = self._calculate_lambda_contributions_fast(numerical_mappings)
# Run sensitivity analysis if requested
sensitivity_analysis = None
if self.config['parameters'].get('run_sensitivity_analysis', False):
sample_size = self.config['parameters'].get('sensitivity_sample_size', 500)
sensitivity_analysis = self.parameter_sensitivity_analysis(sample_size)
# Performance metrics
total_time = time.time() - start_time
performance_metrics = {
'total_execution_time_seconds': total
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## Overview
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## Deployment
# #!/usr/bin/env python3
“””
Quantum Entanglement Validation Framework
This script implements a scientific validation protocol to test whether
any claimed quantum entanglement prediction system actually correlates
with real quantum mechanical entanglement metrics.
Requirements:
pip install qiskit matplotlib numpy scipy
Usage:
python quantum_validation.py
“””
import numpy as np
import matplotlib.pyplot as plt
from scipy.stats import pearsonr
import warnings
warnings.filterwarnings(‘ignore’)
# Qiskit imports
from qiskit import QuantumCircuit, Aer, transpile, assemble
from qiskit.quantum_info import Statevector, partial_trace, entropy, concurrence
from qiskit.quantum_info import random_statevector, DensityMatrix
class QuantumEntanglementValidator:
“””
Scientific validation framework for quantum entanglement prediction systems.
“””
def init(self): self.simulator = Aer.get_backend("statevector_simulator") self.test_cases = [] self.results = []
def generate_bell_state(self, phi=0, theta=0): """Generate parameterized Bell states for testing.""" qc = QuantumCircuit(2) qc.h(0) qc.cx(0, 1)
# Add rotation for parameterized states
if phi != 0:
qc.rz(phi, 0)
if theta != 0:
qc.ry(theta, 1)
return self._get_statevector(qc)
def generate_separable_state(self, alpha=0, beta=0): """Generate separable (non-entangled) states.""" qc = QuantumCircuit(2) qc.ry(alpha, 0) qc.ry(beta, 1) return self._get_statevector(qc)
def generate_mixed_state(self, entanglement_level=0.5): """Generate mixed states with varying entanglement.""" # Create a partially entangled state qc = QuantumCircuit(2) qc.h(0) qc.cry(2 * np.arccos(np.sqrt(entanglement_level)), 0, 1) return self._get_statevector(qc)
def _get_statevector(self, qc): """Helper to get statevector from quantum circuit.""" tqc = transpile(qc, self.simulator) qobj = assemble(tqc) result = self.simulator.run(qobj).result() return result.get_statevector()
def calculate_true_metrics(self, state): """Calculate true quantum entanglement metrics.""" # Convert to density matrix if needed if isinstance(state, Statevector): rho = DensityMatrix(state) else: rho = state
# Get reduced density matrix (trace out qubit 1)
reduced_rho = partial_trace(rho, [1])
# Calculate entanglement entropy (von Neumann)
ent_entropy = entropy(reduced_rho, base=2)
# Calculate concurrence
conc = concurrence(state)
return {
'entropy': ent_entropy,
'concurrence': conc,
'state_description': str(type(state).__name__)
}
def mock_sdkp_predictor(self, state, photon_angle=0): """ Mock implementation of the SDKP formula for testing. This simulates what a claimed predictor might output.
E_AB = w1 * SDN_sim + w2 * ΔVEI + w3 * Δ_QF + w4 * H_QCC
"""
# Generate mock parameters (these would be the invented terms)
np.random.seed(42) # For reproducibility
# Mock "SD&N similarity" - just use photon angle
sdn_sim = np.cos(photon_angle)**2
# Mock "Vibrational Entanglement Index" - random number
delta_vei = np.random.uniform(0, 1)
# Mock "Quantum Flow difference" - another random component
delta_qf = np.random.uniform(-0.5, 0.5)
# Mock "QCC Entropy" - yet another random term
h_qcc = np.random.uniform(0, 0.8)
# Mock weights
w1, w2, w3, w4 = 0.3, 0.2, 0.25, 0.25
# The claimed formula
e_ab = w1 * sdn_sim + w2 * delta_vei + w3 * delta_qf + w4 * h_qcc
return max(0, min(1, e_ab)) # Clamp to [0,1]
def run_comprehensive_test(self): """Run comprehensive validation test suite.""" print("🔬 Quantum Entanglement Validation Framework") print("=" * 50)
test_cases = []
true_metrics = []
predicted_scores = []
# Test Case 1: Perfect Bell States
print("\n📊 Test Case 1: Bell States (Maximally Entangled)")
for i in range(5):
phi = i * np.pi / 4
state = self.generate_bell_state(phi=phi)
metrics = self.calculate_true_metrics(state)
prediction = self.mock_sdkp_predictor(state, photon_angle=phi)
test_cases.append(f"Bell φ={phi:.2f}")
true_metrics.append(metrics['concurrence'])
predicted_scores.append(prediction)
print(f" φ={phi:.2f}: True Concurrence={metrics['concurrence']:.3f}, "
f"Predicted E_AB={prediction:.3f}")
# Test Case 2: Separable States
print("\n📊 Test Case 2: Separable States (No Entanglement)")
for i in range(5):
alpha = i * np.pi / 8
beta = (i + 1) * np.pi / 8
state = self.generate_separable_state(alpha=alpha, beta=beta)
metrics = self.calculate_true_metrics(state)
prediction = self.mock_sdkp_predictor(state, photon_angle=alpha)
test_cases.append(f"Separable α={alpha:.2f}")
true_metrics.append(metrics['concurrence'])
predicted_scores.append(prediction)
print(f" α={alpha:.2f}, β={beta:.2f}: True Concurrence={metrics['concurrence']:.3f}, "
f"Predicted E_AB={prediction:.3f}")
# Test Case 3: Mixed States (Partial Entanglement)
print("\n📊 Test Case 3: Mixed States (Partial Entanglement)")
for level in [0.1, 0.3, 0.5, 0.7, 0.9]:
state = self.generate_mixed_state(entanglement_level=level)
metrics = self.calculate_true_metrics(state)
prediction = self.mock_sdkp_predictor(state, photon_angle=0)
test_cases.append(f"Mixed {level}")
true_metrics.append(metrics['concurrence'])
predicted_scores.append(prediction)
print(f" Level={level}: True Concurrence={metrics['concurrence']:.3f}, "
f"Predicted E_AB={prediction:.3f}")
# Statistical Analysis
print("\n📈 Statistical Analysis")
print("=" * 30)
correlation, p_value = pearsonr(true_metrics, predicted_scores)
print(f"Pearson Correlation: {correlation:.4f}")
print(f"P-value: {p_value:.4f}")
# Validation Criteria
print(f"\n✅ Validation Criteria:")
print(f" • Correlation > 0.9: {'✓' if correlation > 0.9 else '✗'} ({correlation:.4f})")
print(f" • P-value < 0.05: {'✓' if p_value < 0.05 else '✗'} ({p_value:.4f})")
print(f" • Bell states → High scores: {'✓' if np.mean(predicted_scores[:5]) > 0.7 else '✗'}")
print(f" • Separable → Low scores: {'✓' if np.mean(predicted_scores[5:10]) < 0.3 else '✗'}")
# Overall Assessment
criteria_met = (correlation > 0.9 and p_value < 0.05 and
np.mean(predicted_scores[:5]) > 0.7 and
np.mean(predicted_scores[5:10]) < 0.3)
print(f"\n🎯 Overall Assessment:")
if criteria_met:
print("✅ PASS: The predictor shows strong correlation with quantum mechanics")
else:
print("❌ FAIL: The predictor does not align with quantum entanglement")
# Create visualization
self.plot_results(test_cases, true_metrics, predicted_scores, correlation)
return {
'correlation': correlation,
'p_value': p_value,
'passes_validation': criteria_met,
'true_metrics': true_metrics,
'predicted_scores': predicted_scores
}
def plot_results(self, test_cases, true_metrics, predicted_scores, correlation): """Create visualization of validation results.""" plt.figure(figsize=(12, 8))
# Scatter plot
plt.subplot(2, 2, 1)
plt.scatter(true_metrics, predicted_scores, alpha=0.7, s=60)
plt.plot([0, 1], [0, 1], 'r--', alpha=0.5, label='Perfect Correlation')
plt.xlabel('True Concurrence')
plt.ylabel('Predicted E_AB')
plt.title(f'Correlation: {correlation:.4f}')
plt.legend()
plt.grid(True, alpha=0.3)
# Bar comparison
plt.subplot(2, 2, 2)
x = np.arange(len(test_cases))
width = 0.35
plt.bar(x - width/2, true_metrics, width, label='True Concurrence', alpha=0.7)
plt.bar(x + width/2, predicted_scores, width, label='Predicted E_AB', alpha=0.7)
plt.xlabel('Test Cases')
plt.ylabel('Score')
plt.title('Side-by-Side Comparison')
plt.xticks(x, [tc[:8] for tc in test_cases], rotation=45)
plt.legend()
plt.grid(True, alpha=0.3)
# Residuals
plt.subplot(2, 2, 3)
residuals = np.array(predicted_scores) - np.array(true_metrics)
plt.scatter(true_metrics, residuals, alpha=0.7)
plt.axhline(y=0, color='r', linestyle='--', alpha=0.5)
plt.xlabel('True Concurrence')
plt.ylabel('Residuals (Predicted - True)')
plt.title('Residual Analysis')
plt.grid(True, alpha=0.3)
# Distribution comparison
plt.subplot(2, 2, 4)
plt.hist(true_metrics, bins=10, alpha=0.7, label='True Concurrence', density=True)
plt.hist(predicted_scores, bins=10, alpha=0.7, label='Predicted E_AB', density=True)
plt.xlabel('Score')
plt.ylabel('Density')
plt.title('Distribution Comparison')
plt.legend()
plt.grid(True, alpha=0.3)
plt.tight_layout()
plt.show()
def main():
“”“Main execution function.”””
validator = QuantumEntanglementValidator()
results = validator.run_comprehensive_test()
print(f"\n📋 Summary:") print(f"This validation framework tests any claimed entanglement predictor") print(f"against real quantum mechanics. The mock SDKP predictor used here") print(f"fails validation (correlation: {results['correlation']:.4f})") print(f"because it uses non-physical parameters.")
print(f"\n🔬 To test the actual SDKP system:") print(f"Replace 'mock_sdkp_predictor()' with the real implementation") print(f"and run the same validation protocol.")
if **name** == “**main**”:
main()
My project is live at:
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