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Bell State — Quick Recipe

Create and measure the simplest entangled state in quantum computing.

What It Does

A Bell state is a maximally entangled two-qubit state. When measured, both qubits always collapse to the same value — either both |00⟩ or both |11⟩, each with 50% probability. This is the foundation of quantum teleportation, superdense coding, and many quantum algorithms.

The Circuit

q0: ─ H ─ ● ─ M ─
          │
q1: ──── CX ─ M ─
  1. H on qubit 0 → creates superposition (|0⟩ + |1⟩)/√2
  2. CX (CNOT) → entangles qubit 1 with qubit 0
  3. Measure → collapses both qubits simultaneously

Code

from quanta import circuit, H, CX, measure, run

@circuit(qubits=2)
def bell(q):
    H(q[0])
    CX(q[0], q[1])
    return measure(q)

result = run(bell, shots=1024)
print(result.summary())

Expected Output

Measurement Results (1024 shots):
  |00⟩ : ████████████████████ 512 (50.0%)
  |11⟩ : ████████████████████ 512 (50.0%)

Key insight: You'll never see |01⟩ or |10⟩ — that's entanglement! The qubits are correlated, not independent.

Try Next

  • Add noise: run(bell, shots=1024, noise=NoiseModel().add(Depolarizing(p=0.01)))
  • Try the GHZ state: extend to 3+ qubits with more CX gates
  • Visualize: from quanta.visualize_svg import draw_svg; draw_svg(bell, "bell.html")

See Also