发表机构
University of Illinois at Urbana-Champaign; University of Waterloo; Perimeter Institute for Theoretical Physics（伊利诺伊大学厄巴纳-香槟分校; 滑铁卢大学; 理论物理前沿研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究通过zonotopes和zonoids框架刻画量子信道对测量不相容性的破坏与保持，给出量子比特单信道破坏不相容性的充要条件，证明两个破坏信道并行时的超激活现象，并证明匹配维度下保持不相容性等价于酉变换。
AI 中文摘要
如果一个量子信道总是破坏量子测量的不相容性，则称其为不相容性破坏信道。在另一个极端，存在从不破坏不相容性的不相容性保持信道。本研究通过zonotopes和zonoids的数学框架研究这两类信道，该方法为二分测量提供了相容性的完整刻画，并且在量子比特设置中特别有效。利用zonoids的语言，我们给出了量子比特单信道为不相容性破坏的充分必要条件，这些条件对于非单信道也是充分的。作为我们的主要结果之一，我们展示了两个不相容性破坏的量子比特信道在并行使用时不再是不相容性破坏的超激活现象。将此结果转化为量子导引任务，它表明两个两量子比特Werner态副本可以在噪声阈值$1/2$处被导引，尽管仅使用一个副本是不可能的。对于不相容性保持问题，我们证明具有匹配输入和输出维度的量子信道保持一般不相容性当且仅当它是酉变换。当输出维度更大时，该结果不再成立，我们提出了一个一般不相容性保持信道的猜想形式。
英文摘要
A quantum channel is called incompatibility-breaking if it always destroys the incompatibility of quantum measurements. On the other extreme are incompatibility-preserving channels, which never destroy incompatibility. This work studies both types of channels through the mathematical framework of zonotopes and zonoids, an approach that provides a complete characterization of compatibility for dichotomic measurements and is particularly powerful in the qubit setting. Using the language of zonoids, we present necessary and sufficient conditions for when a qubit unital channel is incompatibility-breaking, which are also sufficient for nonunital channels. As one of our main results, we demonstrate the superactivation phenomenon of two incompatibility-breaking qubit channels that are no longer incompatibility-breaking when used in parallel. Translating this result into the task of quantum steering, it says that two copies of a two-qubit Werner state can be steered at noise threshold $1/2$, even though this is impossible using just one copy. For the problem of incompatibility preservation, we prove that a quantum channel with matching input and output dimensions will preserve general incompatibility if and only if it is a unitary transformation. When the output dimension is larger, this result no longer holds, and we offer a conjectured form of a general incompatibility-preserving channel.
