Expected output:

The measurement result is always in the subspace orthogonal to s = 11.
s · z = 0 mod 2 means z_0 XOR z_1 = 0, so valid outcomes are 00 and 11.

Expected output (1024 shots, approximate):
{'00': ~512, '11': ~512}

You should NEVER see '01' or '10'.

After collecting results, solve the linear system:
- z = 11 gives the equation: s_0 XOR s_1 = 0, i.e., s_0 = s_1
- Combined with s ≠ 00, this gives s = 11. ✓

Multiple runs give independent samples from {00, 11}.
With O(n) non-trivial samples, you can determine s by Gaussian elimination.