Holonomy for Quantum Channels

Details Holonomy for Quantum Channels Holonomy for Quantum Channels

2007-11-14

arxiv.org/abs/0711.2140v2

Phys. Rev. A 77, 012114 (2008)

Physics

Quantum Physics

Minor changes, journal reference added

Scientific paper

10.1103/PhysRevA.77.012114

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 Jamio{\l}kowski 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 $4\pi$ rotation symmetry of the neutron spin, can be viewed as early experimental realizations of the channel holonomy.

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