Stage 3 · Lesson 9 of 17
Entanglement
1 · Big question
What makes the Bell-state circuit more than two separate random qubits?
- Build H(q0) followed by CX(q0,q1).
- Predict the ideal Bell outcomes 00 and 11 with equal probability.
- Compare Bell outcomes with two independent H preparations.
- Explain that entanglement cannot send usable information faster than light.
2 · Before we begin
Ideas to bring with you
- Correlation alone does not prove entanglement.
- Two-qubit bit order must be stated.
3 · New words
Meet the words before we use them
- entanglement
- A property of some joint quantum states that cannot be described as separate independent qubit states.
- Bell state
- A maximally entangled two-qubit state; this lesson prepares (|00⟩+|11⟩)/√2.
- no-signalling
- The rule that entanglement cannot be used to send a chosen usable message faster than light.
4 · Simple explanation
Build one idea at a time
Apply H to q0 of |00⟩, then CX with q0 as control and q1 as target. The ideal joint state is the Bell state (|00⟩+|11⟩)/√2.
In the standard basis, the ideal circuit gives 00 and 11 with probability one half each, and zero probability for 01 and 10.
Each individual result is unpredictable, yet the pair is perfectly matched in this basis. The joint state cannot be replaced by two separate pure qubit states, but it still cannot carry a chosen faster-than-light message.
Watch it happen
Bell-state circuit and comparison
Build H(q0)→CX(q0,q1), predict, sample repeated outcomes and compare independent H qubits.
Text description of the animation
With displayed order q1q0, the Bell circuit has P(00)=0.5, P(11)=0.5 and zero for 01 and 10. Independent H qubits have 0.25 for all four strings.
- Predict all four Bell probabilities.
- Run 100 seeded Bell shots and check the allowed outcomes.
- Switch to independent H preparations and compare the four bars.
Evidence to calculate or record: The ideal Bell simulation uses only 00 and 11, while independent H qubits use all four outcomes.
Predict
Commit to an idea before the reveal
Which joint outcomes do you expect from the ideal Bell circuit, and how does that differ from independent H qubits?
Choose a prediction to enable the experiment.
Try it
Correlated or independent?
Predict all four Bell probabilities.
Make and lock a prediction first.
Bit-order legend
Pi Leo labels wires q0, q1 and q2 from top to bottom. In displayed result strings, the highest-numbered bit is written on the left, so a two-qubit result is shown as q1q0. This matches the convention used in the Pi Leo simulator and common Qiskit count strings.
8 · Observe
What did the result actually show?
Look at the displayed values before reading the explanation. Record a pattern, an exception or something that changed.
Bell samples contain only 00 and 11 in the ideal model. Independent samples can contain 00, 01, 10 and 11.
9 · Explain the result
Connect the evidence to the idea
The Bell state is a joint quantum state rather than two separate state descriptions. Local results alone remain random, so one party cannot choose a result to encode an instant message.
10 · Model and limitation
Useful model, honest boundary
The circuit and joint-probability table accurately show the ideal computational-basis prediction.
This one-basis histogram illustrates Bell-state correlation but does not by itself demonstrate every Bell-test property or depict physical particles communicating.
11 · Common mix-ups
Careful wording prevents big mistakes
Entangled particles tell each other what to do.
The joint state predicts correlations without a message between particles.
Entanglement enables faster-than-light communication.
No-signalling prevents chosen usable messages this way.
00 and 11 prove every deep property of entanglement.
A computational-basis histogram alone is limited evidence.
12 · Real quantum-computing connection
Where this appears in circuit work
Bell-state circuits are building blocks for protocols, calibration studies and error-detection ideas, but physical devices add noise and imperfect operations.
13 · Show me moreOptional deeper explanation
Show me more
A full Bell test compares correlations across several measurement settings. The simple computational-basis circuit prepares an entangled state but is not the entire Bell-test experiment.
Try this
Explain the deeper idea in your own words, including one limitation.
14 · Quick summary
Keep these ideas
- H then CX prepares the ideal Bell state.
- Ideal outcomes are 00 and 11 equally.
- Independent H qubits produce four outcomes.
- Entanglement cannot send faster-than-light messages.
Ten-question quiz
Check the ideas—not decorative details
Feedback appears after submission. Retry whenever you like; 8/10 or above means “Topic understood”.
Sources and accuracy notes3 checked references · reviewed 2026-08-15
These records identify the claim each source supports. External documentation can change; dated platform claims were checked on the shown access date.
- Quantum informationIBM Quantum Learning · Multiple systems · accessed 2026-08-15
Supports quiz questions ql-09-q-01, ql-09-q-06, ql-09-q-07, ql-09-q-10 and their related lesson explanations about compound quantum systems; tensor products; multi-qubit states.
- Entanglement and correlationsMicrosoft Learn · Entanglement and correlation · accessed 2026-08-02
Supports quiz questions ql-09-q-02, ql-09-q-03, ql-09-q-05, ql-09-q-08 and their related lesson explanations about compound-system states; entanglement; quantum correlations.
- Quantum Computation and Quantum InformationCambridge University Press · 2010 · Sections 1.2–1.3 and Chapters 4, 6 and 8 · accessed 2026-08-02
Supports quiz questions ql-09-q-04, ql-09-q-09 and their related lesson explanations about quantum states and circuits; quantum algorithms; teleportation, noise and error correction.
- This model is deliberately limited: This one-basis histogram illustrates Bell-state correlation but does not by itself demonstrate every Bell-test property or depict physical particles communicating.
- Predictions, simulations and physical-hardware evidence are labelled separately.