The *GHZ state* (|000⟩ + |111⟩)/√2 extends the Bell pair to three qubits: all agree, all 0 or all 1.

Two states can give the same outcomes and still differ. (|000⟩ − |111⟩)/√2 measures exactly like the GHZ state, but the minus sign is a *relative phase* between its two parts, and a later gate can turn that phase into a different outcome. A distribution cannot see it.

So this exercise states its intent as a state: *prepares*. The engine runs your program and its own reference from |0…0⟩ and compares the two states up to a global phase (a phase on the whole state, which no measurement can see), and the verdict is a proof. Two programs can prepare the same state and still be different circuits, so more than one answer passes.

On the command line an intent is a file:

```sh runnable
cat > pair.qasm <<'QASM'
OPENQASM 3.0;
include "stdgates.inc";
qubit[2] q;
bit[2] c;
h q[0];
cx q[0], q[1];
c = measure q;
QASM
echo '{"distribution": {"00": 0.5, "11": 0.5}}' > pair-intent.json
wai-quantum run pair.qasm --intent pair-intent.json --shots 100
```