Two-qubit circuit that prepares a maximally entangled Bell pair. Measuring one qubit determines the other.
A Bell state cannot be written as a product |ψ⟩ ⊗ |φ⟩. The four Bell states {|Φ+⟩, |Φ-⟩, |Ψ+⟩, |Ψ-⟩} form an orthonormal basis for two qubits and are the resource behind teleportation and superdense coding.
The construction is Hadamard on the first wire, then CX onto the second. Optional X/Z before or after that skeleton select which Bell state you get. This page uses the default |Φ+⟩ = (|00⟩ + |11⟩)/√2.
How it works
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1
Superposition
H on q0 maps |0⟩ to |+⟩. The two-qubit state is (|00⟩ + |10⟩)/√2.
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2
Entangle
CX [0,1] copies the control onto the target. |10⟩ becomes |11⟩, which yields (|00⟩ + |11⟩)/√2.
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3
Readout
Z-basis shots are 00 or 11 with equal probability. The reduced state of either qubit alone is completely mixed.
H 0 CX [0,1]
Function form: Bell("phi_plus")
State. |Φ+⟩ = (|00⟩ + |11⟩)/√2
P(00) = P(11) = 1/2. Never 01 or 10. Outcomes on q0 and q1 are perfectly correlated.
| Basis | Amplitude | Probability |
|---|---|---|
|00⟩ |
1/√2 |
|
|11⟩ |
1/√2 |
Notes
- |Φ-⟩: X on q0 before H.
- |Ψ+⟩: X on q1 before H.
- |Ψ-⟩: X on q1 before H, then Z on q1 after CX.
- Ket labels are |q1 q0⟩ with q0 the rightmost bit, matching the simulator.
Change parameters
The write-up above is for the default circuit. Use this control to generate other variants and load them in the simulator.