arXiv 0711.21402007-11quant-ph

量子信道的完整性

Holonomy for Quantum Channels

David Kult, Johan Åberg, Erik Sjöqvist

备注：: Minor changes, journal reference added
发表信息：: Phys. Rev. A 77, 012114 (2008)
DOI：: 10.1103/PhysRevA.77.012114

摘要：

量子完整性反映了量子力学系统的某些基本结构的曲率，例如与量子态相关的曲率。在这里，我们将完整性的概念扩展到量子信道的家族，即，保迹完全正映射。通过使用Jamioenkowski同构，我们表明，建议的通道holonomy相关的Uhlmann holonomy。一般的理论说明了具体的例子。我们提出了一个物理实现的信道完整性的干涉。这使我们能够确定一个规范不变的物理对象，直接涉及到通道holonomy。在光滑参数化通道族的情况下，描述了平行输运条件和伴随的规范结构。最后，我们指出，干涉仪测试，已在过去进行确认的$4π$旋转对称的中子自旋，可以被视为早期的实验实现的通道完整性。

英文摘要：

A quantum holonomy reflects the curvature of some underlying structure of quantum mechanical systems, such as that associated with quantum states. Here, we extend the notion of holonomy to families of quantum channels, i.e., trace preserving completely positive maps. By the use of the Jamiołkowski isomorphism, we show that the proposed channel holonomy is related to the Uhlmann holonomy. The general theory is illustrated for specific examples. We put forward a physical realization of the channel holonomy in terms of interferometry. This enables us to identify a gauge invariant physical object that directly relates to the channel holonomy. Parallel transport condition and concomitant gauge structure are delineated in the case of smoothly parametrized families of channels. Finally, we point out that interferometer tests that have been carried out in the past to confirm the $4π$ rotation symmetry of the neutron spin, can be viewed as early experimental realizations of the channel holonomy.

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