Physicists introduced the notion of the quantum magic square

They cannot be as easily characterized as their 'classical' cousins.

The magic squares reflect the magic of mathematics. Magic Squares are square grids with a special arrangement of numbers in them. These numbers are special because every row, column, and diagonal adds up to the same number.

Recently, quantum physicist Gemma De las Cuevas and mathematicians Tim Netzer and Tom Drescher introduced the quantum magic square notion. For the first time, physicists studied the properties of this quantum version of magic squares in detail.

Tim Netzer and Tom Drescher from the Department of Mathematics and Gemma De las Cuevas from the Department of Theoretical Physics have introduced the quantum magic square, which is a magic square. Still, instead of numbers, one puts in matrices. This is a non-commutative, and thus quantum, a generalization of a magic square.

In the study, physicists show that quantum magic squares cannot be as quickly characterized as their “classical” cousins. More precisely, quantum magic squares are not convex combinations of quantum permutation matrices. Instead, they are richer and more complicated to understand.

Tom Drescher said“This is the general theme when generalizations to the non-commutative case are studied.”

“The work is at the intersection of algebraic geometry and quantum information and showcases the benefits of interdisciplinary collaboration.”

Journal Reference:
  1. Gemma De las Cuevas et al. Quantum magic squares: Dilations and their limitations, Journal of Mathematical Physics (2020). DOI: 10.1063/5.0022344

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