QLunch: Aabhas Gulati
Speaker: Aabhas Gulati, University of Toulouse
Title: Entanglement in the Dicke Subspace
Abstract: In this talk, I will present some of the recent results in the entanglement properties of mixtures of Dicke states
These quantum states form an important subclass of bosonic states arising in the study of indistinguishable particles.
I first give a background on polynomial positivity and sum of squares, and discuss multipartite entanglement in bosonic states. Then, I will discuss how to encode the mixtures of Dicke states as a symmetric tensor, enabling a direct translation between entanglement properties and well-studied convex cones of tensors.
Within this framework, I will show how separability corresponds to completely positive tensors, the PPT property to moment tensors, entanglement witnesses to copositive tensors, and decomposable witnesses to sums-of-squares tensors.
By using this dictionary, we can obtain constructions of explicit PPT entangled states for systems of three or more qutrits, that refute a recent conjecture in J. Math. Phys. 66, 022203 (2025). Also, these correspondences allow us to show that in mixtures of Dicke states, the PPT condition with respect to the most balanced bipartition implies PPT with respect to any other bipartition.
This work has been done in collaboration with Ion Nechita from CNRS, LPT Toulouse and Clément Pellegrini from IMT Toulouse.