论文标题
关于分组计算的区分性的注释
Notes on distinguishability of postselected computations
论文作者
论文摘要
在量子计算研究中，选择后的框架在各个最近的方向上变得越来越重要。选择后渲染可以执行通用量子计算的简单计算模型。这是线性光学模型首先观察到的[E. Knill，R。Laflamme，G。J. Milburn，Nature 409，46（2001）]，此后为我们提供了许多近期候选人的量子优势，并通勤计算[M. J. Bremner，R。Jozsa，D。J。Shepherd，Proc。 R. Soc。 A 467，459（2011）是第一个。为了促进在选择后存在错误的讨论，我们定义并表征了痕量诱导的距离和钻石距离的计算。我们展示了对任何距离度量的简单属性的反例；凸度的特性（仅考虑纯态输入就足够），合同性和错误的亚粘附性。从积极的一面来看，我们证明了某些较弱的合同性和亚辅助性版本，并且在后选择的设置中保留了许多其他属性。我们通过“转换引理”来实现这一目标，该“转换引理”将任何不等式从标准设置转化为标准设置。
The framework of postselection is becoming more and more important in various recent directions in Quantum Computation research. Postselection renders simple computational models able to perform general quantum computation. This was first observed for the linear optics model [E. Knill, R. Laflamme, G. J. Milburn, Nature 409, 46 (2001)], and has since provided us with many near-term candidates for the quantum advantage, commuting computations [M. J. Bremner, R. Jozsa, D. J. Shepherd, Proc. R. Soc. A 467, 459 (2011)] being the first. To facilitate the discussion of errors in the presence of postselection, we define and characterize trace-induced distance and diamond distance of postselected computations. We show counterexamples to simple properties that one would expect of any distance measure; the properties of convexity (when considering only the pure-state inputs would suffice), contractivity, and subadditivity of errors. On the positive side, we prove that certain weaker versions of contractivity and subadditivity and a number of other properties are preserved in the postselected setting. We achieve this via a "conversion lemma" that translates any inequality from the standard to the postselected setting.
