Energy–time uncertainty relation for driven quantum systems

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https://iopscience.iop.org/article/10.1088/1751-8113/46/33/335302/meta

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10.1088/1751-8113/46/33/335302
 http://hdl.handle.net/11603/19394

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UMBC Physics Department
UMBC Joint Center for Earth Systems Technology (JCET)

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2013-07-29

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journal articles preprints
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Sebastian Deffner and Eric Lutz, Energy–time uncertainty relation for driven quantum systems, Journal of Physics A: Mathematical and Theoretical, Volume 46, Number 33, doi:10.1088/1751-8113/46/33/335302

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© 2013 IOP Publishing Ltd

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Abstract

We derive generalizations of the energy–time uncertainty relation for driven quantum systems. Using a geometric approach based on the Bures length between mixed quantum states, we obtain explicit expressions for the quantum speed limit time, valid for arbitrary initial and final quantum states and arbitrary unitary driving protocols. Our results establish the fundamental limit on the rate of evolution of closed quantum systems.