Holonomy for quantum channels
2008 (English)In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 77, no 1, 012114- p.Article in journal (Refereed) Published
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 Jamiolkowski 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.
Place, publisher, year, edition, pages
2008. Vol. 77, no 1, 012114- p.
Geometric phase, quantum holonomy, completely positive maps, quantum channels, Uhlmann holonomy, mixed quantum states, quantum interferometry, Jamiolkowski isomorphism
Research subject Physics
IdentifiersURN: urn:nbn:se:uu:diva-96152DOI: 10.1103/PhysRevA.77.012114ISI: 000252862000029OAI: oai:DiVA.org:uu-96152DiVA: diva2:170629