基于约化内积博弈的非最大纠缠态的鲁棒自检验
Robust self-testing of nonmaximal entanglement from a reduced inner product game
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中文总结 AI 辅助
本文将内积博弈从六维约化到五维，证明其能鲁棒自检验非最大纠缠态及全部测量效应，并得出最大纠缠态无法完美获胜的结论。
中文摘要 AI 辅助
我们将Lalonde的伪心灵感应内积博弈从六维约化到五维，保留其四个Alice问题和三个Bob问题，并将每个答案字母表减少到五个。我们证明约化后的博弈自检验其非最大纠缠态以及全部35个测量效应。该自检验也是鲁棒的：对于以至少$1-\varepsilon$概率获胜的策略，我们得到$d_{\mathrm{ext}}\le\min\{1,2^{21}\sqrt{\varepsilon}\}$，其中$d_{\mathrm{ext}}=\sqrt{1-\Xi}$，$\Xi$是在局部提取信道下与参考态的最优平方保真度。紧致性论证随后给出在常见局部等距下态上所有测量动作的同时定性鲁棒性。作为自检验的结果，任何有限维的最大纠缠态都无法完美赢得该博弈。
英文摘要
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 $1-\varepsilon$ we obtain $d_{\mathrm{ext}}\le\min\{1,2^{21}\sqrt{\varepsilon}\}$, where $d_{\mathrm{ext}}=\sqrt{1-Ξ}$ 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.
发表机构
- Quantum Science Center of Guangdong–Hong Kong–Macao Greater Bay Area（粤港澳大湾区量子科学中心）
机构由 AI 辅助整理，请以论文原文为准。
