Entanglement
Distinguish a coherent Bell state from classical correlation.
Intuition
In a Bell pair, the joint pure state cannot be separated into a pure state for each qubit. Computational-basis outcomes agree, even though each qubit by itself gives a random result.
Matching 00/11 counts alone does not prove entanglement: a classical mixture can match them. The Bell state's coherent amplitudes also produce correlations in other bases. The judge checks the full pure state, including relative phase.
The mathematics
Look a little deeper
The reduced density matrix of either Bell qubit is maximally mixed, which puts its local Bloch vector at the sphere's center. The joint state is still pure. These correlations do not allow faster-than-light communication.
Use it
Create a Bell pair. Inspect both reduced states under Bloch and joint amplitudes under Statevector.
This exercise uses the same server-side state and circuit checks as its linked practice problem.
Build your circuit
Click a gate to append it, or drag it onto a wire. CX uses the selected control; SWAP uses it as the second operand. Basis order: |qₙ … q₀⟩.
Returned logical circuit · before transpilation · q0 on top
Connect to code
qc.h(0) qc.cx(0, 1)
These operations go inside a circuit-building program. Practice problems provide a complete solve() template.
Check your understanding
First complete the circuit exercise successfully.