prof. dr hab. Karol Życzkowski (UJ): Thirty-six entangled officers of Euler: quantum solution of a classically impossible problem

Friday Jun 3, 2022, 10:15 AM → 11:00 AM Europe/Warsaw

Abstract:

A  quantum combinatorial design is composed of quantum states, arranged with a certain symmetry and balance. Such designs determine distinguished quantum measurements and can be applied for  quantum information processing.Negative solution to the famous problem of 36 officers of Euler implies that there are no two orthogonal Latin squares of order six.We show that the problem has a solution, provided the ranks and the units of each officer can be entangled,  and construct quantum orthogonal Latin squares of this size.   The solution can be visualized on a chessboard of size six, which shows that 36 officers are split in nine groups, each containing of four entangled states.  This design provides a unique example of extremal quantum state and allows  us to construct an original quantum error detection code.

References:

[1] S.A Rather, A.Burchardt, W. Bruzda, G. Rajchel-Mieldzioć, A. Lakshminarayan
and K. Życzkowski, Thirty-six entangled officers of Euler,{\sl Phys. Rev. Lett.} {\bf 128}, 080507 (2022).
[2] D. Garisto, Euler’s 243-Year-Old ‘Impossible’ Puzzle Gets a Quantum Solution,Quanta Magazine, Jan. 10, 2022;     https://www.quantamagazine.org/

Important: This seminar is held in building D-11 room 104. 

03062022-KarolZyczkowski-QuantumComputing.pdf