# Physics Colloquium: Prof. Karol Życzkowski - Thirty-six entangled officers of Euler: Quantum solution of a classically impossible problem

### Center for Theoretical Physics, PAS, Warsaw and Jagiellonian University, Cracow

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 officers are entangled, and construct orthogonal quantum Latin squares of this size. The solution can be visualized on a chessboard of size six, which shows that 36 officers are splitted in nine groups, each containing of four entangled states. It allows us to construct a pure nonadditive quhex quantum error detection code.

### Quanta Magazine: Euler’s 243-Year-Old ‘Impossible’ Puzzle Gets a Quantum Solution

### Time & Location

Jan 13, 2023 | 03:00 PM c.t. - 05:00 PM

Lecture hall A (room 1.3.14), Department of Physics, Arnimallee 14, 14195 Berlin

### Further Information

### Keywords

- colloquium
- entangled state
- Euler
- Karol Życzkowski
- mathematical physics
- physical review letters
- puzzle
- quantum physics
- quantum solution
- research
- science
- theoretical physics
- Thirty-six Entangled Officers of Euler