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.
Related
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- Sparse anisotropic positive maps for qutrit entanglement: exact indecomposability and PPT geometry
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BibTeX
@misc{dahbi2026exact,
title = {{Exact entanglement trade-offs in qutrit and composite-dimensional stabilizer states}},
author = {Zakaria Dahbi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2605.05167},
eprint = {2605.05167},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.05167},
}
RIS
TY - UNPB
TI - Exact entanglement trade-offs in qutrit and composite-dimensional stabilizer states
AU - Zakaria Dahbi
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2605.05167
UR - https://arxiv.org/abs/2605.05167
AB - 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.
ER -