Years 3–6 · Week 9 of 12
Two Qubits and Entanglement
Learning goals
By the end, you can…
- Describe two qubits using a combined state.
- Identify entanglement as a property of some combined quantum states.
- Build an ideal Bell-pair circuit with H and CNOT.
- Explain why entanglement cannot send usable messages faster than light.
What you already know
Connect to a familiar idea
One qubit has a quantum state. With two qubits, quantum theory describes the pair together, including patterns that cannot be assigned to each qubit alone.
- Build a one-qubit H circuit.
- Interpret repeated 0-and-1 measurement counts.
Opening story
Start with something familiar
An ideal circuit prepares two qubits, then measures them many times. The pair produces 00 or 11, never 01 or 10. The individual result is uncertain, but the two results are strongly correlated.
Plain-English explanation
Build the idea carefully
Describe the pair together
Two qubits have a combined quantum state with four computational-basis outcomes: 00, 01, 10 and 11. Some combined states are entangled, so the complete state belongs to the pair rather than separate states for each qubit.
Entanglement gives quantum correlations
An H gate followed by CNOT can prepare a Bell state whose ideal computational-basis measurements give correlated 00 and 11 outcomes. Entanglement does not let either side choose an outcome, so it cannot carry a usable faster-than-light message.
Try the model
Create an ideal Bell pair
Place H on the first qubit and CNOT across the pair. Run one shot, then run many shots and inspect all four outcome bars.
Qubit 0 is the least-significant state-vector bit. Displayed basis labels read q(n−1)…q0.
Ready. Adjust a control, then run the model.
What this model shows: The noiseless simulator shows an ideal Bell state. Real experiments include imperfections and require careful analysis.
Text alternative for this interactive
Trace the printed Bell circuit and interpret a supplied four-bar result chart.
Expected observation: Repeated ideal measurements produce only 00 and 11, with roughly equal counts, while 01 and 10 stay at zero.
Guided activity
Find the correlation
- Predict which of 00, 01, 10 and 11 will appear.
- Run the ideal Bell circuit one hundred times.
- Calculate how many runs have matching and non-matching outcomes.
Evidence to collect: The ideal chart contains matching 00 and 11 results and no 01 or 10 results, while neither side can choose whether a run gives 0 or 1.
Glossary
Words to know
- combined state
- One quantum description for two or more systems together.
- entanglement
- A property of a combined quantum state that cannot be described by separate states for each part.
- correlation
- A pattern showing that results are related.
- CNOT
- A two-qubit gate controlled by one qubit and targeted at another.
Short recap
Keep these ideas
- Two qubits are described by one combined state.
- A Bell circuit can create an entangled state with strong correlations.
- Entanglement does not enable faster-than-light communication.
Knowledge check
4 clear questions
Choose an answer for immediate feedback. You may retry, and your best submitted score is kept.
Explore More Optional extension for Years 5–6
The ideal Bell state used here gives 00 and 11 with equal probability in the computational basis. Other measurement choices reveal more of why entanglement cannot be replaced by a simple matching-card story.
Try this
Compare a pre-matched classical card pair with the Bell-pair result chart. List what the card analogy explains and what it cannot establish.
Adult support Teacher and parent notes
Discuss
- Always show all four outcomes, including zero-height bars.
- Say 'correlated' rather than 'the first tells the second what to do'.
- Repeat the no-signalling statement whenever learners suggest instant messages.
Answer guidance
Look for a combined state, H plus CNOT, ideal 00/11 correlations and the inability to control either local result.
Offline activity
Use a printed circuit and pre-generated data. Matching cards may introduce correlation only if their classical limitation is explicit.
Safety
No entangled-light apparatus is required. Real optical experiments may use lasers and should be handled only by trained staff.
Sources and further reading
Checked references for this lesson
These sources support the lesson’s main scientific claims. Links open on the source organisation’s site.
- Quantum information IBM Quantum Learning · official learning module · checked 2026-08-02
- Entanglement and correlations Microsoft Learn · official documentation · checked 2026-08-02
- Circuits IBM Quantum Learning · official learning module · checked 2026-08-02
- Basics of Quantum Information IBM Quantum Learning · official course · checked 2026-08-02
Content review: Reviewed on 2026-08-02.