Two-qubit causal structures and the geometry of positive qubit-maps
Two-qubit causal structures and the geometry of positive qubit-maps
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DOI：
10.1088/1367-2630/aad612
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发表时间：
2018-03
影响因子：
3.3
通讯作者：
Jonas M. Kübler;D. Braun
中科院分区：
文献类型：
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作者：
Jonas M. Kübler;D. Braun
我们在Ried等人提出的一个装置中研究量子因果推理（2015 Nat. Phys. 11 414），其中共因方案可以与因果方案混合，并且发现量子力学可以在区分这两种方案方面带来优势：而在经典统计学中，需要随机试验等干预措施，如果共同原因来自最大纠缠态，那么量子观测方案就足以检测因果结构。我们分析了这种设置的几何单位的积极的，但不完全积极的量子位映射，所产生的混合量子位通道和转向地图。我们发现的范围内的混合参数，可以产生给定的相关性，并证明了量子优势，在一个更一般的设置，允许任意的unital通道和初始状态与完全混合的约化状态。这是通过建立新的边界上签署的奇异值的总和矩阵。基于几何形状，我们根据观察到的相关性来量化和识别量子优势的起源，并讨论额外的约束如何导致问题的唯一解决方案。
We study quantum causal inference in a setup proposed by Ried et al (2015 Nat. Phys. 11 414) in which a common cause scenario can be mixed with a cause–effect scenario, and for which it was found that quantum mechanics can bring an advantage in distinguishing the two scenarios: whereas in classical statistics, interventions such as randomized trials are needed, a quantum observational scheme can be enough to detect the causal structure if the common cause results from a maximally entangled state. We analyze this setup in terms of the geometry of unital positive but not completely positive qubit-maps, arising from the mixture of qubit channels and steering maps. We find the range of mixing parameters that can generate given correlations, and prove a quantum advantage in a more general setup, allowing arbitrary unital channels and initial states with fully mixed reduced states. This is achieved by establishing new bounds on signed singular values of sums of matrices. Based on the geometry, we quantify and identify the origin of the quantum advantage depending on the observed correlations, and discuss how additional constraints can lead to a unique solution of the problem.