Quantum Information Lab

3 qubits · no measurement

All 8 basis states

Circuit3 / 40 gates

Qubits

Gate

Qubit

Sequence

H0,CNOT0-1,CNOT1-2

Metrics

Total317 / 500

ENTANGLEMENT67

What is entanglement?

Established physics

Split the register down the middle and ask how much of what you know about the whole you would lose by only looking at one half. For a product state, nothing: each half has its own definite description. For an entangled state, the halves have no separate descriptions at all.

Try — Build H then CNOT — two gates — and watch this hit 100. Then apply H to both qubits instead and watch it read 0 while superposition reads 100.

BELL VIOLATION0

What is bell violation?

Established physics

Some correlations are too strong for any story in which each particle carried its answers with it all along. This measures how far past that limit your first two qubits go. Zero does not mean "nearly" — it means a classical explanation still fits.

Try — Build a GHZ state on three qubits: more entangled than a Bell pair, and this reads 0. Its two-qubit marginal is separable, so there is genuinely nothing here to violate an inequality with.

SUPERPOSITION57

What is superposition?

Established physics

How many of the possible outcomes the state actually reaches. A register sitting in one definite pattern scores 0; one spread evenly across every pattern scores 100. This is about spread, and spread alone.

Try — Put H on every qubit, then read this against entanglement: 100 and 0. If you take one thing from this module, take that these are different properties.

FIDELITY100

What is fidelity?

Established physics

Did you build one of the states that has a name? This is the overlap with the closest of a small set of standard states — a Bell or GHZ state, a W state, or the uniform superposition.

Try — Run an empty two-qubit circuit and watch fidelity read 50. Nothing has been built; half the overlap with a Bell state is simply free.

ECONOMY93

What is economy?

Computational experiment

Fewer gates is better. That is the whole metric — it scores restraint, not achievement.

Try — Reach a full CHSH violation in two gates. It is possible — H then CNOT — and the fact that the cheapest non-classical thing costs two gates is worth knowing.

Closest named state: GHZ. A Bell violation of 0 means no violation at all, not a small one — no separable state can produce any.

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Three things people call the same thing

Superposition, entanglement and non-classical correlation get used interchangeably almost everywhere outside a physics department, and they are three different properties. A register with a Hadamard on every qubit is spread across every possible outcome and entangled with nothing. A GHZ state is more entangled than a Bell pair and violates no Bell inequality between any two of its qubits. This module scores them separately so the differences are visible rather than asserted.

The gate set is deliberately discrete — no rotation gates — which means no trigonometry is evaluated anywhere and every amplitude is exact arithmetic on decimal literals. That is what lets the server re-run your circuit and get bit-identical numbers, which is the same contract every other module here holds.

An exact simulation of an idealised circuit: no noise, no decoherence, no measurement. The quantum mechanics is standard and the Bell inequality has been violated in laboratories with the loopholes closed — but nothing here tells you anything about a physical device.