Robust self-testing of nonmaximal entanglement from a reduced inner product game
Abstract
We reduce Lalonde's pseudo-telepathy inner product game from six to five dimensions, keeping its four Alice questions and three Bob questions and reducing each answer alphabet to five. We prove that the reduced game self-tests its nonmaximally entangled state and all 35 measurement effects. The self-test is also robust: for a strategy winning with probability at least 1−ε we obtain dext≤min{1,221√ε}, where dext=√(1−Ξ) and Ξ is the optimal squared fidelity with the reference state under local extraction channels. A compactness argument then gives simultaneous qualitative robustness for all measurement actions on the state under common local isometries. As a consequence of the self-test, no maximally entangled state of any finite dimension can win the game perfectly.
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BibTeX
@misc{chen2026robust,
title = {{Robust self-testing of nonmaximal entanglement from a reduced inner product game}},
author = {Ranyiliu Chen},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.24349},
eprint = {2609.24349},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.24349},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Robust self-testing of nonmaximal entanglement from a reduced inner product game
AU - Ranyiliu Chen
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2609.24349
UR - https://arxiv.org/abs/2609.24349
AB - We reduce Lalonde's pseudo-telepathy inner product game from six to five dimensions, keeping its four Alice questions and three Bob questions and reducing each answer alphabet to five. We prove that the reduced game self-tests its nonmaximally entangled state and all 35 measurement effects. The self-test is also robust: for a strategy winning with probability at least 1−ε we obtain d_ext≤min{1,2^21√ε}, where d_ext=√(1−Ξ) and Ξ is the optimal squared fidelity with the reference state under local extraction channels. A compactness argument then gives simultaneous qualitative robustness for all measurement actions on the state under common local isometries. As a consequence of the self-test, no maximally entangled state of any finite dimension can win the game perfectly.
ER -