Stage 3 · Lesson 8 of 17
Linked quantum systems
1 · Big question
How can two outputs be linked, and why does a link alone not prove entanglement?
- Compare independent and classically matched output patterns.
- Identify control and target in a two-qubit operation.
- Trace CX on basis-state inputs.
- Explain why correlation alone is not proof of entanglement.
2 · Before we begin
Ideas to bring with you
- Two qubits have four basis labels: 00, 01, 10 and 11.
- CX uses distinct control and target roles.
3 · New words
Meet the words before we use them
- correlation
- A pattern in which two recorded variables are statistically related.
- independent
- Prepared so one result pattern does not depend on the other.
- joint system
- Two or more systems described and measured together.
4 · Simple explanation
Build one idea at a time
Two classical objects can be matched in advance, so correlated outputs are not automatically quantum.
Two independently prepared equal-chance bits can produce 00, 01, 10 and 11. Two classically matched bits can be arranged to produce only 00 and 11.
A two-qubit circuit can use one qubit as a CX control and the other as target. A later lesson will show the additional evidence needed to identify an entangled state.
Watch it happen
Independent, matched and quantum-linked comparisons
Switch among three preparations, step through the control-target action and compare joint outcome tables.
Text description of the animation
Three labelled panels compare independent equal-chance outputs, pre-matched classical outputs and an H-plus-CX quantum circuit reserved for the next lesson.
- Inspect the independent output table.
- Create a classical matched-output rule.
- Build the H-CX circuit without naming its state yet, and list what extra evidence would be needed.
Evidence to calculate or record: Both classical matching and the quantum circuit can show 00/11 in one basis, so one correlation table alone is insufficient proof.
Predict
Commit to an idea before the reveal
If a result table contains only 00 and 11, does that pattern by itself prove the source was entangled?
Choose a prediction to enable the experiment.
Try it
Classify the source
Inspect the independent output table.
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.
Independent outputs can fill all four rows. Classical matching and the selected quantum circuit can share the same two visible rows in this measurement basis.
9 · Explain the result
Connect the evidence to the idea
Correlation describes data. Entanglement is a property of a joint quantum state and cannot be inferred from every correlated table without suitable preparation and measurement evidence.
10 · Model and limitation
Useful model, honest boundary
The comparison prevents a familiar classical pattern from being mistaken for uniquely quantum evidence.
The classical cards and quantum circuit are teaching models; matching one measurement table does not make their underlying descriptions identical.
11 · Common mix-ups
Careful wording prevents big mistakes
Any matching outputs prove entanglement.
Classical systems can be correlated too.
CX sends a message from one person to another.
CX is a joint gate inside a circuit, not a communication service.
The control qubit is always physically above the target.
Diagram placement is a convention; roles must be labelled explicitly.
12 · Real quantum-computing connection
Where this appears in circuit work
Multi-qubit circuit design states qubit roles and bit ordering so controls, targets and displayed outcome strings are not silently reversed.
13 · Show me moreOptional deeper explanation
Show me more
Entanglement tests use carefully chosen measurements and statistical comparisons. A single computational-basis histogram is not enough to establish every property.
Try this
Explain the deeper idea in your own words, including one limitation.
14 · Quick summary
Keep these ideas
- Classical outputs can be correlated.
- Independent equal-chance pairs can show four outcomes.
- CX has control and target roles.
- Correlation alone does not prove entanglement.
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-08-q-02, ql-08-q-05, ql-08-q-06 and their related lesson explanations about compound quantum systems; tensor products; multi-qubit states.
- CircuitsIBM Quantum Learning · Quantum circuits — Circuits · accessed 2026-08-15
Supports quiz questions ql-08-q-03, ql-08-q-07, ql-08-q-10 and their related lesson explanations about classical and quantum circuit models; gates and wires; standard-basis measurement.
- Entanglement and correlationsMicrosoft Learn · Entanglement and correlation · accessed 2026-08-02
Supports quiz questions ql-08-q-01, ql-08-q-04, ql-08-q-08, ql-08-q-09 and their related lesson explanations about compound-system states; entanglement; quantum correlations.
- This model is deliberately limited: The classical cards and quantum circuit are teaching models; matching one measurement table does not make their underlying descriptions identical.
- Predictions, simulations and physical-hardware evidence are labelled separately.