Consistency of the Adiabatic Theorem

• DOI: 10.1007/s11128-004-7712-7
• Publication Date: 2004-12-02T02:05:39Z
• Authors: M. S. Sarandy; L.-A. Wu; D. A. Lidar
• Keywords: Argument (complex analysis); Adiabatic theorem; Adiabatic Quantum Computation; Quantum no-deleting theorem

We review the quantum adiabatic approximation for closed systems, and its recently introduced generalization to open systems (M.S. Sarandy and D.A. Lidar, e-print quant-ph/0404147). We also critically examine a recent argument claiming that there is an inconsistency in the adiabatic theorem for closed quantum systems [K.P. Marzlin and B.C. Sanders, Phys. Rev. Lett. 93, 160408 (2004)] and point out how an incorrect manipulation of the adiabatic theorem may lead one to obtain such an inconsistent result.<br/>v3: 11 pages, no figures. Published version. This pedagogical work is part comment on, part simplification of the paper "Inconsistency in the application of the adiabatic theorem" by K.-P. Marzlin and B.C. Sanders, Phys. Rev. Lett. 93, 160408 (2004)<br/>