Years 11–12 · Week 1 of 12
Classical and Quantum Information
Learning goals
By the end, you can…
- Distinguish a physical information carrier from the information state used to describe it.
- Represent uncertainty about a classical bit with a probability distribution.
- Explain why a qubit state is not the same object as a 0-or-1 measurement result.
- Compare deterministic, probabilistic and quantum information processing.
What you already know
Connect to a familiar idea
You have used bits, probabilities and physical devices that store information. This lesson separates the device, its state and the classical result that a measurement records.
- Fractions, decimals and probabilities that add to one
- Reading a two-entry column vector
- The idea that a computer bit can represent 0 or 1
Opening story
Start with something familiar
A phone can store one bit using a physical device, but the symbol 0 is not the device itself. Quantum computing keeps the same distinction: the qubit is a physical system, its quantum state is a mathematical description, and a measurement produces recorded classical data.
Plain-English explanation
Build the idea carefully
Three layers: system, state and result
Information is physical because it must be represented by a physical system. A classical bit state is labelled 0 or 1, while a probability vector (p₀, p₁) describes uncertainty about which value will be found; p₀ and p₁ are non-negative and p₀ + p₁ = 1. A deterministic classical operation maps each allowed input to one output. A probabilistic operation can produce different outputs with stated probabilities. These descriptions remain classical because each recorded output is an ordinary classical value.
From probability vectors to qubit states
A pure qubit state can be written |ψ⟩ = α|0⟩ + β|1⟩. The vertical-bar symbols are ket notation for state vectors; |0⟩ and |1⟩ are the computational-basis vectors. The complex-number entries α and β are probability amplitudes, not two stored classical answers. Measuring in this basis records either 0 or 1, with probabilities determined by them. A state is a preparation-dependent mathematical object used to predict measurement statistics. One result does not reveal an unknown state completely, so scientists repeat a controlled preparation and measurement when estimating probabilities.
Try the model
Classical bit and qubit comparison lab
Choose a classical probability distribution or a qubit preparation, then run repeated measurements and compare the resulting histograms.
Ready. Adjust a control, then run the model.
What this model shows: The qubit panel is an educational state-vector simulation, not execution on real quantum hardware.
Text alternative for this interactive
Text alternative: a classical distribution (0.5, 0.5) and the qubit states (|0⟩ + |1⟩)/√2 and (|0⟩ − |1⟩)/√2 all give equal 0/1 probabilities in this basis, although the two qubit states behave differently after suitable gates.
Expected observation: Both panels record ordinary 0-or-1 outcomes, but only the qubit state includes amplitudes whose relative phase can affect a later gate sequence.
Guided activity
Classify the description
- Sort twelve cards into physical system, state description or measurement result.
- For each state card, identify whether it is classical probabilistic or quantum.
- Choose two preparations with the same immediate 0/1 probabilities.
- Explain what further experiment could distinguish the two preparations.
Evidence to collect: A completed classification table and an explanation that repeated measurements after a basis-changing gate can reveal a phase-dependent difference between two qubit states.
Glossary
Words to know
- bit
- A classical unit of information with allowed values 0 and 1.
- probability distribution
- A list of non-negative outcome probabilities that add to one.
- physical system
- The material device or object used to carry information.
- quantum state
- A mathematical description used to predict outcomes of quantum measurements.
- qubit
- A two-level quantum system used to represent quantum information.
- amplitude
- A real or complex number in a quantum state from which probabilities are calculated.
- measurement
- A physical process that produces a classical outcome and can change the state.
Short recap
Keep these ideas
- A physical carrier is not the same thing as its information state.
- Classical probabilities describe uncertainty about classical outcomes.
- A qubit state contains amplitudes and is not a pair of stored answers.
- Measurement converts information about a chosen quantum observable into a recorded classical result.
Knowledge check
7 clear questions
Choose an answer for immediate feedback. You may retry, and your best submitted score is kept.
Mathematical Extension Optional extension for Year 12
Write a classical probability vector as p = [p₀, p₁]ᵀ and a pure qubit state as |ψ⟩ = [α, β]ᵀ. Compare the restrictions p₀ + p₁ = 1 and |α|² + |β|² = 1, and explain why amplitudes permit phase-dependent interference while probabilities do not.
Try this
Construct two normalised state vectors with identical computational-basis probabilities but different relative phases. Predict a gate sequence that distinguishes them, then check it in the simulator.
Adult support Teacher and parent notes
Discuss
- Why is the symbol 0 not a complete description of the device storing it?
- What can repeated results tell us that one result cannot?
- Why should a simulation be labelled separately from real hardware?
Answer guidance
Look for explicit separation of carrier, state and outcome. Strong answers say that amplitudes are not probabilities and identify relative phase as operationally meaningful.
Offline activity
Use three sets of cards labelled system, state and result. Students sort examples, then justify any card whose category depends on context.
Safety
This lesson uses only a browser simulation and paper sorting. No laboratory apparatus, personal data or public student posting is required.
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.
- Basics of Quantum Information IBM Quantum Learning · official course · checked 2026-08-02
- Classical information IBM Quantum Learning · official learning module · checked 2026-08-02
- Quantum information science National Institute of Standards and Technology · government explainer · checked 2026-08-02
Content review: Reviewed on 2026-08-02.