A complete theory of multipartite entanglement in diagonally symmetric bosonic states

A complete theory of multipartite entanglement in diagonally symmetric bosonic states

Seminar author:Aabhas Gulati

Event date and time:10/30/2025 02:30:pm

Event location:Seminars Room, GIQ

Event contact:

We study the highly symmetric class of mixed states also known as mixtures of dicke states or diagonally symmetric states. These states are an important subset of bosonic states with local unitary local symmetries. We study the entanglement properties of these states,that can be parametrized by a single symmetric n-legged positive tensor.We show that the separability of such states can be completely characterised in terms of the completely positive tensors, generalising the results from the bipartite case. Moreover, the PPT condition is equivalent to some flattenings of the tensor being positive-semidefinite. Based on the property of sums of squares of polynomials, we also define the notion of sum of squares tensors. We Show that the “indecomposable” witnesses for detecting PPT entanglement can be understood as copositive tensors that are not sum of squares.This allows us to make important connections between the literature in polynomial optimisation, matrix analysis and entanglement theory, and establish a number of important corollaries. We show that in this class of highly symmetric states, there is no bound entanglement in qubits. Wealso find PPT entangled states in three qutrits, while also constructing new bosonic entanglement witnesses. We also show that the PPT across the largest bipartition implies PPT across all bipartitions.