Based on the quantum-memory-assisted entropic uncertainty relation (QMA-EUR), we study the quantum phase transition (QPT) of a spin-1/2 frustrated Heisenberg chain and show that QMA entropy can be a useful tool to detect QPT. For the six-site case, we choose the reduced two-site as the detecting system and obtain the analytical result of QMA entropy and its bound. We find that the QMA entropy of the ground state is discontinuous at the first-order QPT point. Meanwhile for the excited state, the catastrophe point of QMA entropy approaches the infinite-order QPT point, which is confirmed by the numerical results in the 8-, 10- and 12-site cases. Moreover, we study the behavior of QMA entropy undergoing the dephasing process. Interestingly, two-site QMA entropy can still indicate the QPT point when the state degenerates into a mixed state. In this sense, QMA entropy is more effective than quantum correlation in reflecting the quantum criticality.

中文翻译：

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自旋1/2海森堡链的熵不确定性关系和量子相变

基于量子记忆辅助的熵不确定性关系（QMA-EUR），我们研究了自旋1/2失意的海森堡链的量子相变（QPT），并证明了QMA熵可以作为检测QPT的有用工具。对于六点情况，我们选择简化的两点作为检测系统，得到QMA熵及其边界的分析结果。我们发现，基态的QMA熵在一阶QPT点处是不连续的。同时，对于激发态，QMA熵的突变点接近无穷次QPT点，这在8、10和12位情况下的数值结果得到了证实。此外，我们研究了相移过程中QMA熵的行为。有趣的是，当状态退化为混合状态时，两点QMA熵仍可以指示QPT点。