Linearity and Quantum Adiabatic Theorem

Zhaohui Wei; Mingsheng Ying

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arXiv · quant-ph/0701135

Linearity and Quantum Adiabatic Theorem

Zhaohui Wei·Mingsheng Ying

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Abstract

We show that in a quantum adiabatic evolution, even though the adiabatic approximation is valid, the total phase of the final state indicated by the adiabatic theorem may evidently differ from the actual total phase. This invalidates the application of the linearity and the adiabatic approximation simultaneously. Besides, based on this observation we point out the mistake in the traditional proof for the adiabatic theorem. This mistake is the root of the troubles that the adiabatic theorem has met. We also show that a similar mistake remains in some recent modifications of the traditional adiabatic theorem attempting to eliminate the troubles.

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Zhaohui Wei, Mingsheng Ying. 2007-02-17. Linearity and Quantum Adiabatic Theorem. https://arxiv.org/abs/quant-ph/0701135

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