Monogamy of Entanglement Bounds and Improved Approximation Algorithms for Qudit Hamiltonians
Zackary Jorquera, Alexandra Kolla, Steven Kordonowy, Juspreet Singh Sandhu, and Stuart Wayland
Quantum 10, 2088 (2026). https://doi.org/10.22331/q-2026-04-28-2088 We prove new monogamy of entanglement bounds for two-local qudit Hamiltonians of rank-one projectors without one-local terms. In particular, we certify the maximum energy in terms of the maximum matching of the underlying interaction graph via low-degree sum-of-squares proofs. Algorithmically, we show that a simple matching-based algorithm approximates the maximum energy to at least $1/d$ for general graphs and to at least $1/d