optimize entropy

codes/plot_entropy_and_dim.py

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+import numpy as np
+import matplotlib.pyplot as plt
+from quantum_states import sample_and_calculate
+from tqdm import tqdm
+
+# Define range of dimensions to test
+fixed_dim = 64
+dimensions = np.arange(2, 64, 2)  # Test dimensions from 2 to 50 in steps of 2
+expected_entropies = []
+theoretical_entropies = []
+predicted_entropies = []
+
+# Calculate entropies for each dimension
+for dim in tqdm(dimensions, desc="Calculating entropies"):
+    # For each dimension, we'll keep one subsystem fixed at dim=2 
+    # and vary the other dimension
+    entropies = sample_and_calculate(dim, fixed_dim, n_samples=1000)
+    expected_entropies.append(np.mean(entropies))
+    theoretical_entropies.append(np.log2(min(dim, fixed_dim)))
+    beta = min(dim, fixed_dim)/(2*np.log(2)*max(dim, fixed_dim))
+    predicted_entropies.append(np.log2(min(dim, fixed_dim)) - beta)
+
+# Create the plot
+plt.figure(figsize=(10, 6))
+plt.plot(dimensions, expected_entropies, 'b-', label='Expected Entropy')
+plt.plot(dimensions, theoretical_entropies, 'r--', label='Theoretical Entropy')
+plt.plot(dimensions, predicted_entropies, 'g--', label='Predicted Entropy')
+plt.xlabel('Dimension of Subsystem B')
+plt.ylabel('von Neumann Entropy (bits)')
+plt.title(f'von Neumann Entropy vs. System Dimension, with Dimension of Subsystem A = {fixed_dim}')
+plt.legend()
+plt.grid(True)
+plt.show()