CNRS, Laboratoire de Physique Théorique (LPT) Toulouse
TITLE
[HG_AP] High-dimensional entanglement with positive partial transpose: asymptotic, random, and deterministic approaches
ABSTRACT
Finding PPT (Positive Partial Transpose) quantum states with high Schmidt numbers has recently become a significant mathematical challenge in quantum information theory. In this talk, we introduce and discuss three complementary approaches to address this question: (1) high-dimensional convex geometry, (2) random matrix theory, and (3) duality and representation theory. In the first two parts, we show the existence of sequences of quantum states whose Schmidt number grows linearly with the local dimension. In the third part, by considering the quantum objects having symplectic group symmetry, we provide broad explicit families of d⊗d quantum states with the Schmidt number exactly d/2.