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Geometric phase plays an important role in evolution of pure or mixed quantumstates. However, when a system undergoes decoherence the development ofgeometric phase may be inhibited. Here, we show that when a quantum systeminteracts with two competing environments there can be enhancement of geometricphase. This effect is akin to Parrondo like effect on the geometric phase whichresults from quantum frustration of decoherence. Our result suggests that themechanism of two competing decoherence can be useful in fault-tolerantholonomic quantum computation.

Enhancement of Geometric Phase by Frustration of Decoherence: A Parrondo like Effect