2007/11/30 by David Kult, Johan Åberg, Erik Sjöqvist
Mathematics · Physics and Astronomy · #Atomic and Subatomic Physics Research #Combinatorics #Curvature #Geometry #Holonomy #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Parallel transport #Physics #Pure mathematics #Quantum #Quantum Mechanics and Applications #Quantum mechanics #Theoretical physics #Topology (electrical circuits) #quant-ph
paper · pdf · doi:10.1103/physreva.77.012114
published as Phys. Rev. A 77, 012114 (2008) · Minor changes, journal reference added
openalex publication_date 2008/01/29 · arxiv created 2008/01/30 · arxiv updated 2016/03/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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\lkowski 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\ensuremathπ rotation symmetry of the neutron spin can be viewed as early experimental realizations of the channel holonomy.