[ICQ] Aabhas Gulati (IMT) Entanglement in the Dicke subspace

[ICQ] Aabhas Gulati (IMT) Entanglement in the Dicke subspace
2026-05-05 10:45 - 11:45 (Europe/Paris) | LaBRI
In this talk, I will discuss 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.

We introduce a tensor-based parametrization where the diagonal entries of these states are encoded as a symmetric tensor, enabling a direct translation between entanglement properties and well-studied convex cones of tensors. This dictionary maps separability to completely positive tensors, the PPT property to moment tensors, entanglement witnesses to copositive tensors, and decomposable witnesses to sum of squares tensors.

As corollaries of our main results, we establish that PPT entanglement exists for all multipartite systems with three qutrits or more, disproving a recent conjecture in [J. Math. Phys. 66, 022203 (2025)]. We also show that, for mixtures of Dicke states, the PPT condition with respect to the most balanced bipartition implies PPT with respect to any other bipartition. We further connect bosonic extendibility of mixtures of Dicke states to the duals of known hierarchies for non-negative polynomials, such as the ones by Reznick and Polya. We thus provide semidefinite programming relaxations for separability and entanglement testing in the Dicke subspace.

This is based on the work with Ion Nechita (CNRS, LPT Toulouse) and Clément Pellegrini (IMT Toulouse). The preprint is available at [ https://arxiv.org/abs/2602.15800 | https://arxiv.org/abs/2602.15800 ]

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