Exact entanglement trade-offs in qutrit and composite-dimensional stabilizer states

Abstract

When absolute maximal entanglement is unavailable in a state family, different objectives can select different distributions of residual entanglement. We determine exact trade-offs for qutrit stabilizer states and binary--ternary product states. For eight qutrits, evaluation of the complete published classification gives three nondominated balanced-cut entanglement profiles, characterized by the probabilities of obtaining three or four maximally entangled qutrit pairs. We relate the squared entropy-deficit objective to code weight enumerators and use a uniformity-forcing bound to prove that its eleven-qutrit minimum is six. The unique minimizing Clifford class is an already classified code, whose entropy profile also attains a sharp bound on average reference--erasure mutual information among four-uniform eleven-qutrit stabilizer states. In local dimension six, explicit sector alignments attain 56 maximally mixed four-party reductions, the maximum for arbitrary binary--ternary product states. Within the stabilizer product family, the exact cost--count Pareto boundary consists of $(44,48)$ and $(48,56)$. These results identify when aggregate optimization determines operational entanglement properties and when it does not. Published classifications supply coverage; analytical bounds, explicit witnesses, and independent arithmetic checks establish the stated consequences.

arXiv commentSubstantially revised with new results and reproducibility materials. Title and author list updated