This note complements the paper "One-Way Ticket to Las Vegas and the Quantum Adversary" (arxiv:2301.02003). I develop the ideas behind the adversary bound - universal algorithm duality therein in a different form, using the same perspective as Barnum-Saks-Szegedy in which query algorithms are defined as sequences of feasible reduced density matrices rather than sequences of unitaries. This form may be faster to understand for a general quantum information audience: It avoids defining the "unidirectional relative $\gamma_{2}$-bound" and relating it to query algorithms explicitly. This proof is also more general because the lower bound (and universal query algorithm) apply to a class of optimal control problems rather than just query problems. That is in addition to the advantages to be discussed in Belovs-Yolcu, namely the more elementary algorithm and correctness proof that avoids phase estimation and spectral analysis, allows for limited treatment of noise, and removes another $\Theta(\log(1/\epsilon))$ factor from the runtime compared to the previous discrete-time algorithm.

翻译：本说明补充了论文“拉斯维加斯和量子反射单行票”(arxiv:2301.02003),我以不同的形式发展了对手约束背后的思想-通用算法的二元性,采用了与Barnum-Saks-Szegedy相同的视角,其中查询算法被定义为可行的降低密度矩阵序列而不是单词序列。对于一般量信息受众来说,这种形式可能更快理解:它避免定义“单向相对$\gamma%2}受约束”并明确将其与查询算法联系起来。这一证据也更为笼统,因为较低约束(和通用查询算法)适用于最佳控制问题类别,而不仅仅是查询问题。此外,在Belovs-Yolcu中讨论的优点是避免阶段估测和光谱分析的更基本的算法和正确性证明,允许对噪音进行有限的处理,并且从运行时与以前的离离离离离离离离离离离解算法的另外1美元(\\\\\\\ ipsilon) 系数。