Testing the Quantum Strategy

This page allows you to test the quantum strategy for the game described in "Quantum Pseudo-Telepathy Saves the World" (submitted to Analog Science Fiction and Science Fact).

We'll use the notation from the that paper, and we'll also use two abbreviations: p stands for 1/√2 and q stands for 1/√-2.

The quantum strategy begins with Alice, Bob and Charlie creating a three-qubit quantum computer that is in the state: p|κκκ> + p|γγγ> Click the buttons below to see how the quantum state changes when Alice, Bob and Charlie each run a program that corresponds to receiving a smooth or jagged boulder.

After running Alice's Smooth Program, the state is:

½|κκ κ> + ½|κγ γ> + ½|γκ κ> - ½|γγ γ>

After running Bob's Smooth Program, the state is:

½|κκκ> + ½|κγκ> + ½|γκγ> - ½|γγγ>

After running Charlie's Smooth Program, the state is:

½|κκκ> + ½|κκγ> + ½|γγκ> - ½|γγγ>

After running Alice's Jagged Program, the state is:

½|κκκ> + ½i|κγγ> + ½|γκκ> - ½i|γγγ>
(where i is the imaginary square root of -1)

After running Bob's Jagged Program, the state is:

½|κκκ> + ½|κγκ> + ½i|γκγ> - ½i|γγγ>
(where i is the imaginary square root of -1)

After running Charlie's Jagged Program, the state is:

½|κκκ> + ½|κκγ> + ½i|γγκ> - ½i|γγγ>
(where i is the imaginary square root of -1)

After running Bob's Smooth Program, the state is:

After running Charlie's Smooth Program, the state is:

After running Bob's Jagged Program, the state is:

After running Charlie's Jagged Program, the state is:

After running Bob's Smooth Program, the state is:

After running Charlie's Smooth Program, the state is:

After running Bob's Jagged Program, the state is:

After running Charlie's Jagged Program, the state is:

After running Alice's Smooth Program, the state is:

After running Charlie's Smooth Program, the state is:

After running Alice's Jagged Program, the state is:

After running Charlie's Jagged Program, the state is:

After running Alice's Smooth Program, the state is:

After running Charlie's Smooth Program, the state is:

After running Alice's Jagged Program, the state is:

After running Charlie's Jagged Program, the state is:

After running Alice's Smooth Program, the state is:

After running Bob's Smooth Program, the state is:

After running Alice's Jagged Program, the state is:

After running Bob's Jagged Program, the state is:

After running Alice's Smooth Program, the state is:

After running Bob's Smooth Program, the state is:

After running Alice's Jagged Program, the state is:

After running Bob's Jagged Program, the state is:

After running Alice's Smooth Program, the final state is:

½|κκκ> + ½|κγγ> + ½|γκγ> + ½|γγκ>

This wins because they always keep an odd number of boulders.

After running Bob's Smooth Program, the final state is:

½|κκκ> + ½|κγγ> + ½|γκγ> + ½|γγκ>

This wins because they always keep an odd number of boulders.

After running Charlie's Smooth Program, the final state is:

½|κκκ> + ½|κγγ> + ½|γκγ> + ½|γγκ>

This wins because they always keep an odd number of boulders.

Alice will not have a smooth boulder in this case, because there must be an odd number of smooth boulders.

Bob will not have a smooth boulder in this case, because there must be an odd number of smooth boulders.

Charlie will not have a jagged boulder in this case, because there must be an odd number of smooth boulders.

Alice will not have a smooth boulder in this case, because there must be an odd number of smooth boulders.

Bob will not have a jagged boulder in this case, because there must be an odd number of smooth boulders.

Charlie will not have a smooth boulder in this case, because there must be an odd number of smooth boulders.

After running Alice's Smooth Program, the final state is: