Optimal finite-copy readout of three-qubit entanglement with state retention
Abstract
For unknown three-qubit pure states, we characterize the optimal trade-off among GHZ-class certification, binary probability readout of the three-tangle, and conditional state retention. The vanishing ideal of the null class specifies the optimal certification subspace, while a polynomial multiplication operator gives the spectral limit for binary readout. Four copies are necessary for a nonzero certificate. A fifth copy raises the optimal success probability from τ2/48 to 5τ2/72 and permits the original unknown state to be retained, where τ is the three-tangle. We obtain this gain as an instance of a general symmetry-based additional-copy theorem. At six copies the optimal certification probability is (39+2S)τ2/296, with S=∑XTr ρX2, whereas the largest exact binary probability is τ2/8. Local Schur measurements and conditional local operations with classical communication attain these bounds. Retaining the full six-copy branch record yields a weighted estimator with lower variance than binary thinning of the same data. Explicit circuits and fixed-budget comparisons connect the success probabilities to input-copy consumption, retained quantum output, and coherent gate cost.
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BibTeX
@misc{wu2026optimal,
title = {{Optimal finite-copy readout of three-qubit entanglement with state retention}},
author = {Yu-Xin Wu and Yuan-Hong Tao and Ji-Hui Mo and Peng-Fei Ma and Shu-Hui Wu},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.08233},
eprint = {2611.08233},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.08233},
}
RIS
TY - UNPB
TI - Optimal finite-copy readout of three-qubit entanglement with state retention
AU - Yu-Xin Wu
AU - Yuan-Hong Tao
AU - Ji-Hui Mo
AU - Peng-Fei Ma
AU - Shu-Hui Wu
PY - 2026
DA - 2026/11/05
PB - arXiv
DO - 10.48550/arxiv.2611.08233
UR - https://arxiv.org/abs/2611.08233
AB - For unknown three-qubit pure states, we characterize the optimal trade-off among GHZ-class certification, binary probability readout of the three-tangle, and conditional state retention. The vanishing ideal of the null class specifies the optimal certification subspace, while a polynomial multiplication operator gives the spectral limit for binary readout. Four copies are necessary for a nonzero certificate. A fifth copy raises the optimal success probability from τ^2/48 to 5τ^2/72 and permits the original unknown state to be retained, where τ is the three-tangle. We obtain this gain as an instance of a general symmetry-based additional-copy theorem. At six copies the optimal certification probability is (39+2S)τ^2/296, with S=∑_XTr ρ_X^2, whereas the largest exact binary probability is τ^2/8. Local Schur measurements and conditional local operations with classical communication attain these bounds. Retaining the full six-copy branch record yields a weighted estimator with lower variance than binary thinning of the same data. Explicit circuits and fixed-budget comparisons connect the success probabilities to input-copy consumption, retained quantum output, and coherent gate cost.
ER -