CHSH: Alice & Bob’s Quantum Challenge
The Quantum Turtle · Quantum Play Lab
Alice & Bob's Quantum Challenge
Can two players beat the best classical strategy without talking? Play the CHSH game with classical answers or measurements on an entangled pair. Discover why entanglement changes the odds.
Alice and Bob agree on their answers before receiving random questions. During a round they cannot communicate.
Alice
Receives x and responds with a
Bob
Receives y and responds with b
Agree on a strategy before the questions arrive
Choose the bit each player returns for each possible question. There are 16 deterministic strategies; shared randomness cannot improve the 75% classical limit.
Choose the local measurement settings
Alice and Bob share |Φ⁺⟩ = (|00⟩ + |11⟩)/√2. Each uses only their own question to choose a measurement angle. Different questions are sampled uniformly.
Play a round to see Alice and Bob's questions and answers.
See the four question pairs
| x | y | Win rate for this pair | Rounds played |
|---|
What makes the quantum game different?
The referee chooses independent, uniformly random bits x and y. Alice and Bob cannot communicate after receiving them. A classical strategy can win at most 75% of rounds on average. With shared entanglement and the right measurement settings, the maximum rises to cos²(π/8) ≈ 85.36% (Tsirelson's bound).
For the entangled |Φ⁺⟩ state and real measurement angles α and β, the correlation is E = cos(2(α−β)). The game samples individual outcomes from those quantum probabilities. It does not predetermine a win, and finite samples can be above or below the theoretical limits. Changing settings clears prior results so the observed rate always refers to one strategy.
This is a local browser simulation, not an experiment on quantum hardware. No account or physical separation is required: the game enforces the no-communication rule by generating each answer from only its local question and preselected strategy. Explore more Quantum Play Lab activities.