Quantum 2025 – scientific programme

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MON: Monday Contributed Sessions

MON 9: Quantum Entanglement

MON 9.2: Talk

Monday, September 8, 2025, 14:30–14:45, ZHG101

Analytical structures in high-dimensional entanglement — •Robin Krebs and Mariami Gachechiladze — Technische Universität Darmstadt, Darmstadt, Hesse, Germany

Efficient and generic methods for analyzing high-dimensional entanglement are crucial for scalable and resilient quantum computation and quantum communication protocols. Understanding the necessary mathematical structures requires analyzing high Schmidt number (SN) PPT states. We prove a generalization of the projection property, which relates the Schmidt number of a quantum state with its lower-dimensional projections. Then, we introduce the concept of a local extension, increasing local dimensions and entanglement content. This new method is then used to construct an extreme point of the PPT set in dimensions 4x5 with SN 3, the lowest dimensional known instance of SN 3 PPT entanglement. To accurately detect the SN for such extreme points, a sufficient and necessary generalization of the range criterion is introduced. We also present various examples of the implications of these results for the structure of high-dimensional entanglement.

Keywords: Entanglement; Quantum Information Protocols