Manifestations of quantum holonomy in interferometry

Abstract

Abelian and non-Abelian geometric phases, known as quantum holonomies, have attracted considerable attention in the past. Here, we show that it is possible to associate nonequivalent holonomies to discrete sequences of subspaces in a Hilbert space. We consider two such holonomies that arise naturally in interferometer settings. For sequences approximating smooth paths in the base (Grassmann) manifold, these holonomies both approach the standard holonomy. In the one-dimensional case the two types of holonomies are Abelian and coincide with Pancharatnam's geometric phase factor. The theory is illustrated with a model example of projective measurements involving angular momentum coherent states.

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Cited by in corpus (7)

• Operational approach to the Uhlmann holonomy
• Universal quantum computation and quantum error correction using discrete holonomies
• Non-Abelian generalization of off-diagonal geometric phases
• Holonomy for Quantum Channels
• Correlation induced non-Abelian quantum holonomies
• Non-Abelian off-diagonal geometric phases in nano-engineered four-qubit systems
• Separation of quantum time evolution into holonomic and dynamical parts