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  "path": "/papers/q-2026-04-28-2088/",
  "publishedAt": "2026-04-28T18:41:28.000Z",
  "site": "https://quantum-journal.org",
  "tags": [
    "Paper",
    "https://doi.org/10.22331/q-2026-04-28-2088"
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  "textContent": "Quantum 10, 2088 (2026).\n\nhttps://doi.org/10.22331/q-2026-04-28-2088\n\nWe 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 $1/d + \\Theta(1/D)$ for graphs with bounded degree, $D$. This outperforms random assignment, which, in expectation, achieves energy of only $1/d^2$ of the maximum energy for general graphs. Notably, on $D$-regular graphs with degree, $D \\leq 5$, and for any local dimension, $d$, we show that this simple matching-based algorithm has an approximation guarantee of $1/2$. Lastly, when $d=2$, we present an algorithm achieving an approximation guarantee of $0.595$, beating that of [31], which gave an approximation ratio of $1/2$.",
  "title": "Monogamy of Entanglement Bounds and Improved Approximation Algorithms for Qudit Hamiltonians"
}