Quantum Entanglement Calculator

This calculator quantifies how entangled a two-qubit quantum state is, starting from the four amplitudes you enter for the basis states |00⟩, |01⟩, |10⟩, and |11⟩. It first normalizes those amplitudes so their squared magnitudes sum to 1 (turning them into valid quantum probabilities), then computes concurrence — a standard entanglement measure that equals 0 for any separable state and 1 for a maximally entangled state like a Bell pair, using the formula C = 2|a₀₀a₁₁ − a₀₁a₁₀|. Squaring concurrence gives the tangle, and running concurrence through the entanglement-of-formation relation gives a second measure expressed in bits, both describing the same underlying entanglement from slightly different angles.

Separately, the calculator traces out the second qubit to get a reduced density matrix for the first, then computes its von Neumann entropy — a state with zero entropy is unentangled, while a maximally mixed reduced state (entropy of 1 bit) signals maximal entanglement, mirroring what concurrence already reported. The Bell state fidelity checks how closely your normalized state overlaps with the canonical |Φ+⟩ Bell state specifically, rather than entanglement in general, so a state can be strongly entangled yet score low on this particular fidelity if it's closer to a different Bell state. All of these measures assume you're describing a pure two-qubit state with real-valued amplitudes; genuinely complex amplitudes or mixed states (where the system is entangled with something outside the two qubits you're tracking) require a fuller density-matrix treatment this simplified calculator doesn't attempt.