Tight lower bounds on the time it takes to generate a geometric phase

Abstract

Geometric phase is a concept of central importance in virtually every branch of physics. In this paper, we show that the evolution time of a cyclically evolving quantum system is restricted by the system's energy resources and the geometric phase acquired by the state. Specifically, we derive and examine three tight lower bounds on the time required to generate any prescribed Aharonov-Anandan geometric phase. The derivations are based on recent results on the geometric character of the Mandelstam-Tamm and Margolus-Levitin quantum speed limits.

11 pages, 2 figures, identical to the published article

References in corpus (6)

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• Phase Dynamics of Two Entangled Qubits
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Cited by in corpus (5)

• Margolus-Levitin quantum speed limit for an arbitrary fidelity
• Estimate of the time required to perform a nonadiabatic holonomic quantum computation
• Isoholonomic inequality and tight implementations of holonomic quantum gates
• Parallel transport in rotating frames and projective holonomic quantum computation
• Systems that saturate the Margolus-Levitin quantum speed limit