GHOST GUARD
A quantum error-correction game · Check, don't look · Grades 6–8
Challenge: explain the invisible error
One Sign card changes the secret in a way these Check and Flip cards cannot repair. Your goal is to explain why and name the missing capability. This level does not count toward the duel score.
The Ghost Box
Inside the Ghost Box
Noise Lab
Every night, each coin is hit by noise on its own. After each night the Guardian checks and fixes. How often is the ghost lost?
Lines: exact chance. Dots: your runs. With checks after every night, 3 or 5 coins beat 1 coin only when the flip chance is below 50% (the threshold). Against sign errors a flip guard never helps: more coins make the ghost more likely to sour. Real quantum computers use codes that check for both kinds.
How to play
Goal. The Keeper hides a ghost in the box: a row of three HEADS coins and a row of three TAILS coins, each with its own chips (the secret). The Guardian wins if after seven nights the ghost comes back exactly as it started. The Gremlin wins if it does not.
Hands. Guardian: 3 Check + 4 Rest. Gremlin: 2 Flip + 5 Calm (Level 2: one Calm becomes a Sign). Every night each player plays one card face-down.
| Card | What the Keeper does |
|---|---|
| Calm | Nothing. |
| Flip k | Turns coin k over in both rows. |
| Sign k | In every row whose coin k shows TAILS, swaps every chip's colour. |
| Rest | Nothing. |
| Check | Says only: "Coins 1 & 2 match / don't match. Coins 2 & 3 match / don't match." The answer is the same for both rows. |
| Peek k | Shows coin k, but the ghost must pick one row (chance ∝ chips²). The other row is lost, and so is the secret. |
Check table.
| Coins 1 & 2 | Coins 2 & 3 | Turn |
|---|---|---|
| match | match | nothing |
| don't match | match | coin 1 |
| don't match | don't match | coin 2 |
| match | don't match | coin 3 |
End. After night 7 there is one free final Check and Fix. Then the box opens. Same chips, same colours, same rows: the Guardian wins.
Level 2 is a diagnosis. The single Sign error cannot be repaired by the available Check and Flip cards. Try the short Sign + Check example, compare the chip colours with the secret, then explain what is missing. You can also explore all seven nights. Neither route adds a duel win or loss.
The physics. The two rows are the two parts of one qubit stored in three qubits (the 3-qubit bit-flip code). Chips are amplitudes, colours are signs. Flip is a bit-flip error (X), Sign is a phase error (Z), Check measures the parities Z₁Z₂ and Z₂Z₃, and Peek is a measurement that collapses the superposition. Two flips between checks make the Guardian "fix" the wrong coin and swap the rows: a logical error.
Ghost Guard · QCaMP classroom materials · Works offline. The Level 1 computer uses equilibrium strategies. Level 2 explores the limits of the bit-flip code through an unscored diagnosis.