Quantum magic squares in view of Birkhoff-von Neumann Theorem

Date

2024-8-23

Author

Doğan, Sunay

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Quantum magic squares are generalizations of doubly stochastic matrices to arbitrary, possibly non-commutative algebras, more specifically C∗-algebras. Birkhoff-von Neumann Theorem states that every doubly stochastic matrix is a convex combination of permutation matrices. One inevitable question is whether a quantum magic square is a convex combinations of quantum permutation matrices. It has been proven by Cuevas, Drescher, and Netzer that the generalization of the Birkhoff-von Neumann Theorem in the quantum setting is not true in general. A quantum magic square is a convex combination of Arveson extreme points but not necessarily a convex combination of quantum permutation matrices. Additionally, the relationships between different subsets of quantum magic squares, including their inclusion properties, have been studied in this context.

Subject Keywords

Quantum magic squares, Quantum permutation matrices, Semi-classical magic squares, Birkhoff-von Neumann theorem, Arveson extreme points

URI

https://hdl.handle.net/11511/111013

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Graduate School of Natural and Applied Sciences, Thesis