发表机构
The University of Melbourne（墨尔本大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
从信息论角度研究经典数据的最优量子编码，证明最大量子泄漏是编码策略的通用质量度量，并给出最优编码的构造条件。
AI 中文摘要
从信息论角度研究了用于量子辅助统计推断的经典数据的最优编码。我们证明任何量子计算推断过程的精度受限于从经典数据通过其量子编码的最大量子泄漏，从而将泄漏确立为编码器的通用、任务无关的质量度量。这表明最大量子泄漏是编码策略用于统计推断质量的通用度量，因为它仅依赖于数据的量子编码，而非推断任务本身。证明最优通用编码策略（即最大化最大量子泄漏的编码策略）由纯态实现。当量子比特足够多时，基编码被证明是全局最优的。然而，当系统维度较小时，相位编码是最优的。对于后者，任何紧框架、任何平均态为最大混合态的系综实际上都是最优的。在紧框架中，等角紧框架（ETF）被区分为唯一对称的最优编码，即它们达到Welch下界关于成对重叠的饱和，并具有自参考的最优测量。突出的特例包括量子三态、正则单形和对称信息完备正算子值测度（SIC-POVM），并提供了ETF结构和显式码字构造。数值例子验证了理论预测。
英文摘要
Optimal encoding of classical data for quantum-assisted statistical inference is investigated from an information-theoretic perspective. We prove that the accuracy of any quantum-computing inference procedure is upper bounded by the maximal quantum leakage from the classical data through its quantum encoding, establishing leakage as a universal, task-agnostic quality measure for encoders. The optimal encoding strategy, i.e., an encoding strategy that maximizes the maximal quantum leakage, is proved to be attained by pure states. When there are enough qubits, basis encoding is proved to be universally optimal. However, when the dimension of the system is small, phase encoding is optimal. For the latter, the optimal encoding is not unique. That is, any tight frame, any ensemble whose average state is the maximally mixed state, is in fact optimal. Within tight frames, equiangular tight frames (ETFs) are distinguished as the uniquely symmetric optimal encodings, i.e., they saturate the Welch lower bound on pairwise overlaps. Prominent special cases are the qubit trine, the regular simplex, and symmetric informationally complete positive operator-valued measures (SIC-POVMs), for which the ETF structure and explicit codeword constructions are provided. Numerical examples are presented to validate the theoretical predictions.
CommentsFixed a few mistakes and typos
