AI 中文总结
该研究针对受未知通用幺正扰动的多假设量子态鉴别问题，提出基于最不利先验的方法，可提升最坏情况成功概率并给出干扰参数区域的诊断描述。
AI 中文摘要
我们研究当所有候选量子态均受到相同未知通用幺正扰动影响时的鲁棒K元量子态鉴别问题。该未知扰动并非待识别的标签，而是会改变固定测量性能的干扰因素。我们将该问题表述为针对可能扰动的极小极大决策问题，并提出采用与干扰参数空间上的最不利先验（LFP）相关的贝叶斯最优联合测量。对于该空间的有限离散化，我们证明LFP可通过半定规划计算，且对应值与有限网格极小极大成功概率一致。作为数值演示，我们考虑二元非正交量子比特模型和带有未知通用幺正扰动的非正交三态量子三态模型。与参考点最优测量和均匀先验贝叶斯测量相比，基于LFP的测量大幅拉平了成功概率分布，提升了最坏情况下的成功概率。所得LFP将权重集中于主动限制鲁棒鉴别性能的干扰参数空间区域，从而提供了建设性的测量设计和对困难干扰参数区域的诊断描述。
英文摘要
We study robust K-ary quantum-state discrimination when all candidate states are affected by the same unknown common unitary perturbation. The unknown perturbation does not represent the label to be identified, but acts as a nuisance factor that changes the performance of a fixed measurement. We formulate the problem as a minimax decision problem over the possible perturbations and propose using the Bayes-optimal collective measurement associated with a least favorable prior (LFP) on the nuisance-parameter space. For a finite discretization of this space, we show that the LFP can be computed by a semidefinite program and that the corresponding value coincides with the finite-grid minimax success probability. As numerical demonstrations, we consider a binary nonorthogonal qubit model and a nonorthogonal three-state qutrit model with an unknown common unitary perturbation. The LFP-based measurement substantially flattens the success-probability profile and improves the worst-case success probability compared with a reference-point optimal measurement and a uniform-prior Bayes measurement. The resulting LFP concentrates its weight on regions of the nuisance-parameter space that actively limit the robust discrimination performance, thereby providing both a constructive measurement design and a diagnostic description of the difficult nuisance-parameter regimes.
Comments13 pages, 3 figures
