Institute for Quantum Computing, University of Waterloo, Waterloo, ON, Canada.
Naturwissenschaftlich-Technische Fakultät Universität Siegen, Siegen, Germany.
Nat Commun. 2021 Apr 9;12(1):2129. doi: 10.1038/s41467-021-22275-0.
Given two quantum channels, we examine the task of determining whether they are compatible-meaning that one can perform both channels simultaneously but, in the future, choose exactly one channel whose output is desired (while forfeiting the output of the other channel). Here, we present several results concerning this task. First, we show it is equivalent to the quantum state marginal problem, i.e., every quantum state marginal problem can be recast as the compatibility of two channels, and vice versa. Second, we show that compatible measure-and-prepare channels (i.e., entanglement-breaking channels) do not necessarily have a measure-and-prepare compatibilizing channel. Third, we extend the notion of the Jordan product of matrices to quantum channels and present sufficient conditions for channel compatibility. These Jordan products and their generalizations might be of independent interest. Last, we formulate the different notions of compatibility as semidefinite programs and numerically test when families of partially dephasing-depolarizing channels are compatible.
考虑两个量子信道，我们研究了确定它们是否相容的任务——这意味着可以同时执行两个信道，但在未来，可以选择期望输出的精确一个信道（而放弃另一个信道的输出）。在这里，我们给出了几个关于这个任务的结果。首先，我们表明它等同于量子态边际问题，即每个量子态边际问题都可以重新表述为两个信道的相容性，反之亦然。其次，我们表明相容的测量-准备信道（即，打破纠缠的信道）不一定有一个测量-准备相容化信道。第三，我们将矩阵的 Jordan 积的概念扩展到量子信道，并提出了信道相容性的充分条件。这些 Jordan 积及其推广可能具有独立的兴趣。最后，我们将不同的相容性概念表述为半定规划，并数值测试了部分去相位-去极化信道族的相容性。
