Logic Masters Deutschland e.V.

Puzzle link: Play on SudokuPad.

Short rules:

Normal Sudoku rules apply. The sum of the digits in A_j and B_j, where A_j ≥ B_j, j = 1,...,14, must occur in a cell at the shortest possible Manhattan distance from both A_j and B_j.

Long rules:

Normal Sudoku rules apply. In each cage labeled A_j, where j = 1,...,14, there is a person called Alice_j, who wants to exchange a “quantum key” with a person called Bob_j, who is located in a cage labeled B_j with the same j. For this purpose, a pair of “entangled photons” is created by “spontaneous parametric down-conversion” of a “pump photon” in a cell that contains the frequency of the pump photon, P_j, as a digit. That cell must be located at the shortest possible Manhattan distance from both A_j and B_j, with both distances being equal. The Manhattan distance between two cells is the sum of their vertical and their horizontal separations measured in numbers of cells.

One of the created entangled photons is the “signal” with frequency A_j that is sent to Alice_j and written as a digit in cage A_j, and the other is the “idler” with frequency B_j sent to Bob_j and written as a digit in cage B_j. Due to the conservation of energy, P_j = A_j + B_j, and in addition by convention A_j ≥ B_j for all j.

Your feedback, ratings and comments are highly appreciated. Have fun!

Background: The process of spontaneous parametric down-conversion can indeed be used to create pairs of entangled photons, with energies as stated in the puzzles rules, that in turn are used for quantum key distribution in cryptography.

Example: The following image provides a fully solved example on a 4x4 grid. You may solve the example for yourself here on SudokuPad.