Update entanglement.py

quantum/entanglement.py

@@ -1 +1,72 @@
-print("Hello World")
+from __future__ import annotations
+from dataclasses import dataclass
+import math
+from typing import Tuple
+
+@dataclass
+class BellState:
+    """
+    Represents one of the four maximally entangled Bell states.
+
+    Attributes
+    ----------
+    name : str
+        A human-readable label for the Bell state (e.g., "Φ+", "Ψ-").
+    coefficients : Tuple[complex, complex, complex, complex]
+        The amplitudes for the computational basis |00>, |01>, |10>, |11>.
+    """
+    name: str
+    coefficients: Tuple[complex, complex, complex, complex]
+
+    def is_maximally_entangled(self) -> bool:
+        """
+        Determine whether this state is maximally entangled.
+
+        For a Bell state, this checks that all nonzero coefficients have equal magnitude.
+
+        Returns
+        -------
+        bool
+            True if maximally entangled, False otherwise.
+        """
+        non_zero = [abs(c) for c in self.coefficients if c != 0]
+        return len(non_zero) > 1 and len(set(non_zero)) == 1
+
+
+def create_bell_state(index: int) -> BellState:
+    """
+    Factory function to construct one of the four standard Bell states.
+
+    Parameters
+    ----------
+    index : int
+        Index (0‑3) selecting among Φ+, Ψ+, Ψ-, Φ-.
+
+    Returns
+    -------
+    BellState
+        The requested Bell state.
+
+    Raises
+    ------
+    ValueError
+        If the index is not between 0 and 3.
+    """
+    inv_sqrt2 = 1 / math.sqrt(2)
+    coeffs = {
+        0: (inv_sqrt2, 0, 0, inv_sqrt2),        # Φ+
+        1: (0, inv_sqrt2, inv_sqrt2, 0),        # Ψ+
+        2: (0, inv_sqrt2, -inv_sqrt2, 0),       # Ψ-
+        3: (inv_sqrt2, 0, 0, -inv_sqrt2),       # Φ-
+    }
+    names = ["Φ+", "Ψ+", "Ψ-", "Φ-"]
+    if index not in coeffs:
+        raise ValueError("index must be in range 0‑3 to select a Bell state")
+    return BellState(name=names[index], coefficients=coeffs[index])
+
+
+if __name__ == "__main__":
+    # Example usage: create each Bell state and check entanglement
+    for i in range(4):
+        bell = create_bell_state(i)
+        print(f"{bell.name}: coefficients = {bell.coefficients}, maximally entangled = {bell.is_maximally_entangled()}")