Bonn 2025 – scientific programme

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QI: Fachverband Quanteninformation

QI 5: Quantum Entanglement I

QI 5.4: Talk

Monday, March 10, 2025, 18:00–18:15, HS IX

New methods for high dimensional entanglement in PPT states — •Robin Krebs and Mariami Gachechiladze — Technische Universität Darmstadt, Darmstadt, Hesse, Germany

Creation and manipulation of high dimensional entanglement is fundamental for quantum information protocols. To understand the structure of high-dimensional entanglement and attain the optimal witnesses to certify the entanglement dimension, analyzing the Schmidt Number (SN) of PPT states is necessary, which is notoriously hard to do. In this work, we take a step forward in developing novel methods for finding high SN PPT states. To do this, we work with the so-called projection property of high-dimensional entangled states: Any bound entangled state with SN k can be obtained via local projections on a higher dimensional PPT state with SN (k+1). This larger state can be viewed as an extended state. More generally, this defines a convex cone of PPT extensions of a fixed initial state. Then, the (extremal) intersection geometry of the extension cone and PPT set in the corresponding dimension is investigated. This way, it is possible to obtain new candidates of high SN states. For such extreme points of the PPT set, we derive a necessary and sufficient SN criterion applicable to the extended states. On various examples, we observe that extensions of low degrees do not increase the SN, which constrains the search process. Instead, here, we discover patterns for the original fixed state that lead to high SN extensions. This way, we find the smallest known instance of three-dimensional PPT entanglement in 4× 5-dimensional Hilbert spaces, improving our results for 5× 5-dimensional states.

Keywords: Entanglement; Quantum Information Protocols; Foundations; Entanglement Distillation