The board
The game of fox and hounds (also called “Wolf and Sheep”, “Hounds and Hare”, “Fox
and Geese”, or “Devil and Tailors”) is played on an ordinary checkerboard between the
fox (here it is a cat), who has one black piece, and the hounds, who have four white ones.
The pieces move only diagonally on the white squares (as in Checkers).
Beginning of the game
Initially the four hounds are placed in the last row and the cat in a square in the first row.
The cat always starts.
The moves:
- Levels 1-5:
:
- The cat can move diagonally to all directions, forward and backward. It can move only to empty squares (not occupied by a hound).
The cat's player turn ends after the cat has moved.
- The hounds can move diagonally only forward. They can move only to empty squares (not occupied by a hound or a cat).
The hounds' player turn ends after one hound has moved.
-
Levels 2-5:
:
Splits the cat into a superposition of cats. The cat player's turn ends after all cats have moved.
- Levels 2,3: The cat splits to two superposed cats of equal size/amplitude.
- Levels 4,5: The cat splits to three superposed cats of equal size/amplitude.
- Levels 4,5:
:
A superposed cat flips its phase between positive (solid) and negative (transparent).
- Level 5:
A single hound can move to a square occupied by a superposed cat and become in a superposition.
The hounds' player turn ends when one hound, either classical or quantum, has moved.
The Quantum State:
After the cat is split in levels 4 and 5, the quantum state is described by the position inside each square
i.e. the right, center and left of the square.
In level 5, if a hound is in superposition, then each of the three quantum states (left, center, right) describes a superposed cat
and a superposed hound.
Quantum effects:
- Levels 3,4,5: Measurement
Several turns after the cat is split, a measurement of the cat's position is performed.
The measrument results, i.e. the cat's measured position, is probabilistic according to the superposed cats' size/amplitude.
After the measurement, only one position remains, while the others collapse and disappear.
- Level 3: The measurement is performed 3 turns after the cat is split.
- Level 4: The measurement is performed 5 turns after the cat is split.
- Level 5: The measurement is performed 5 turns after the cat is split.
If a hound is also in a superposition, the hound also collapses according its entanglement with the cat.
The hound that remains is the one whose position inside the square (left, center or right)
corresponds to the remaining cat's position (left, center or right).
- Levels 4,5: Interference
If two quantum states are identical, interference occurs, either constructive or destructive, depending on the cats' phases.
- Level 4: Interference occurs when two (or more) superposed cats occupy the same square.
If they have the same phase (both solid or both transparent), a single cat remains with double the size. (Constructive)
If they have opposit phase (one solid and one transparent), both cats disappear and the third one beomces classical. (Destructive)
- Level 5: Interference occurs when two (or more) quantum states are identical.
How to win:
The cat player wins if (all) cats have passed all the hounds.
The hounds' player wins if (at least one) cat is trapped, i.e. has no possible moves.
If the cat is in a superposition and only one cat is trapped, the game ends with partial win/lose to both players.