Monogamy of Entanglement Bounds and Improved Approximation Algorithms for Qudit Hamiltonians

Abstract.We establish new entanglement monogamy bounds for two-local qudit Hamiltonians and certify ground state energy using sum-of-squares proofs. A simple matching-based algorithm achieves better-than-random approximations, including a 0.595 guarantee for qubits, outperforming prior results on bounded-degree graphs.