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Superposition, entanglement and non-classical correlation are used interchangeably almost everywhere outside a physics department, and they are three different properties of a state. This module scores them separately, on circuits small enough to reason about by hand, so the differences stop being a claim you have to accept and become two numbers side by side on a panel. It is also the one module here whose subject is not speculative at all: the Bell inequality has been violated in laboratories with the loopholes closed.
Before you start — Comfort with the idea that a system can be in a combination of states, and nothing else. No complex arithmetic is asked of you — the panel does it — and no linear algebra is needed until the advanced tier, which states every formula the code computes.
A Hadamard puts one qubit into an equal combination of 0 and 1. Do it to every qubit and the register reaches every possible outcome with equal probability — the busiest-looking state the module can draw. It is also a product state: each qubit has its own complete description, and nothing is correlated with anything.
Do — Open the uniform superposition and read superposition against entanglement: 100 and 0. If you take one thing from this module, take that these are different properties.
A Hadamard followed by a CNOT produces a Bell pair: neither qubit has a state of its own, and measuring one fixes the other. It is the cheapest non-classical object there is, and the entire cost is two gates.
Do — Open the Bell pair. Entanglement reads 100, and so does the Bell violation — this circuit sits exactly at the Tsirelson bound, the most any quantum state can violate the CHSH inequality. Then delete the CNOT and watch both collapse to 0 together.
The CHSH inequality bounds a particular combination of four correlation measurements at 2 — for ANY theory in which each particle carries its answers with it, whatever those hidden answers are. Quantum mechanics reaches 2√2 and no further. The score runs from 0 at the classical bound to 100 at that quantum maximum, so it reads as how far past any classical explanation the state goes.
Do — Note that the gauge reads exactly 0 for every separable state, not "a little". Being at 1.9 is not 95% of a violation — the classical bound is free, and only the part above it means anything.
A GHZ state on three qubits is all-or-nothing: either every qubit is 0 or every one is 1. It is more entangled across the half-split than a Bell pair. Look at only two of its qubits, though, and their joint state is separable — so the CHSH test between them finds nothing at all.
Do — Open the GHZ state and compare entanglement against the Bell violation. Both are true readings of the same state, and neither implies the other. This is the step that stops "entangled" from being one word for one thing.
Economy scores restraint and nothing else, so an empty circuit scores 100 on it and 0 on everything else. Fidelity has a floor too: on two qubits, the untouched state |00> already overlaps a Bell state by half, before a single gate. Every challenge that mentions either metric therefore also requires an achievement — a board that rewarded them alone would be rewarding you for building nothing.
Do — Run an empty two-qubit circuit and read fidelity: 50, for free. Then reach a full Bell violation in two gates and keep economy at 95.
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.
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.
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.
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.
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.
Surfacing sources you can verify is a deliberate anti-pseudoscience measure, not a bibliography. Nothing on this page asks to be taken on trust.
Glossary — every term used above, defined once.