Jonas Britz

---

Quantum entanglement is a fundamental resource in quantum information theory, yet deciding whether a given bipartite quantum state is separable or entangled is computationally intractable in general. In this talk, we consider the Doherty–Parrilo–Spedalieri (DPS) hierarchy of semidefinite approximations for the separable cone in two structured settings: for states with diagonal unitary invariance, and for states with Bose symmetry.

For diagonal unitary invariant states, we show that the hierarchy can be block diagonalized, which leads to a substantially more efficient implementation. For Bose symmetric states, we characterize the dual hierarchy in terms of sums of squares of Hermitian complex polynomials, extending a known result from the unstructured case. In both settings, the completely positive cone CP, its dual COP, and their sums-of-squares-based approximations play a central role.

---

CWI Amsterdam & LAAS-CNRS Toulouse
0.03
Contact: Frank Vallentin