🔔 The CHSH Game
The Bell test behind the 2022 Nobel Prize — 75% for any classical team, 85.4% with entanglement.
dot at the tip: answer 0 · dot at the other end: answer 1
The real Qiskit code
The same game as an interactive Jupyter notebook — the quantum circuit runs on Qiskit, and you can change it.
Opens a free Jupyter session on mybinder.org (via QuBins) — starting it can take a few minutes
git clone the repository, create the conda environment from environment.yml, and open CHSH-Game.ipynb.Alice and Bob each get a random bit and answer with a bit, without talking. They win if their answers are the same — unless both got a 1, then they must differ. No classical strategy wins more than 75% of the rounds: a short parity argument shows that every table of answers loses at least one question.
Sharing one pair of entangled qubits and measuring along well-chosen angles, they win 85.4% — cos²(22.5°), the most quantum mechanics allows (Tsirelson’s bound). Unlike the GHZ game and the magic square, the quantum team still loses some rounds: the advantage shows in the statistics, exactly as in the real Bell tests honored by the 2022 Nobel Prize. The notebook lets you try all 16 classical tables, turn the measurement angles yourself, and see why 75% and 85.4% are the limits.