Jonas Eidesen

• Eidesen, Jonas (2024). Sheaves of measures and KMS-weights on topological graph algebras. Mathematica Scandinavica. ISSN 0025-5521. 130(3), s. 582–606. doi: 10.7146/math.scand.a-144797. Fulltekst i vitenarkiv Vis sammendrag

  We show that the collection of regular Borel measures on a second-countable locally compact Hausdorff space has the structure of a sheaf. With this we give an alternate description of the pullback of a regular Borel measure along a local homeomorphism. We are able to use these tools to give a description of the KMSβ-weights for the gauge-action on the graph C∗-algebra of a second-countable topological graph in terms of sub-invariant measures on the vertex space of said topological graph.

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• Eidesen, Jonas (2025). Projective error models: Stabilizer codes, Clifford codes, and weak stabilizer codes. Fulltekst i vitenarkiv
• Eidesen, Jonas (2025). Projective Error Models: Stabilizer codes, Clifford codes, and weak stabilizer codes. Fulltekst i vitenarkiv
• Eidesen, Jonas (2024). Om Clifford-teori for endelige grupper. Fulltekst i vitenarkiv
• Eidesen, Jonas (2026). Groups and Error Correction in Quantum Communication. Universitetet i Oslo. Fulltekst i vitenarkiv Vis sammendrag

  Quantum error correction is an important component of current scientific efforts towards developing practical realizations of quantum communications. In recent years quantum error correction has also become a melting pot for multiple mathematical disciplines, including representation theory, operator algebras, and noncommutative geometry to name a few. In this thesis we initiate deep investigations into some of the mathematical structures that the field of quantum error correction has to offer. Papers I and II in this thesis investigate the structure of stabilizer codes and Clifford codes using tools from projective representation theory. Paper I serves to establish some technical results, and interesting examples of codes that are best realized using the language of projective representation theory. Paper II builds upon the work of paper I and sets the framework established therein into a broader context. Paper III investigates distances between quantum information-channels from the perspective of noncommutative geometry. The quantum information theoretic properties of stability and chaining are shown to hold for constructions that are natural within noncommutative geometry. The papers are preceded by an introductory section on projective representation theory.

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