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