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Group operator algebras and Non commutative geometry / Algèbres d'opérateurs de groupes et Geometrie non commutative
4 videos

Group operator algebras and Non commutative geometry / Algèbres d'opérateurs de groupes et Geometrie non commutative

Albert Schwarz : Quantum Mechanics and Quantum Field Theory from Algebraic and Geometric Viewpoints
3 videos

Albert Schwarz : Quantum Mechanics and Quantum Field Theory from Algebraic and Geometric Viewpoints

Not Only Scalar Curvature Seminar
60 videos

Not Only Scalar Curvature Seminar

Clément Delcamp : Topological Symmetry and Duality in Quantum Lattice Models
4 videos

Clément Delcamp : Topological Symmetry and Duality in Quantum Lattice Models

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Combinatorics and Arithmetic for Physics: special days 2023

Collection Combinatorics and Arithmetic for Physics: special days 2023

Organizer(s) Gérard H. E. DUCHAMP, Maxim KONTSEVICH, Gleb KOSHEVOY, Sergei NECHAEV and Karol A. PENSON
Date(s) 15/11/2023 - 17/11/2023
linked URL https://www-lipn.univ-paris13.fr/~duchamp/Conferences/CAP10_2023.html
00:00:00 / 00:00:00
7 27

Thirty-six entangled officers of Euler:quantum solution of a classically impossible combinatorial problem

By Karol Zyczkowski

A quantum combinatorial designs is composed of quantum states, arranged with a certain symmetry and balance. They 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 [1,2]. 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 [3]. It allows us to construct a pure nonadditive quhex quantum error detection code.

Information about the video

  • Date of recording 15/11/2023
  • Date of publication 20/11/2023
  • Institution IHES
  • Language English
  • Audience Researchers
  • Format MP4

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Bibliography

  • [1] S.A Rather, A.Burchardt, W. Bruzda, G. Rajchel-Mieldzioc, A. Lakshminarayan and K. Zyczkowski, Thirty-six entangled officers of Euler, Phys. Rev. Lett. 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/
  • [3] K. Zyczkowski, W. Bruzda, G. Rajchel-Mieldzioc, A. Burchardt, S. A. Rather, A. Lakshminarayan, 9 × 4 = 6 × 6: Understanding the quantum solution to the Euler’s problem of 36 officers, J. Phys.: Conf. Series 2448, 012003 (2023).

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