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arXiv:1507.05848 · Physical Review X

Generalized Geometric Quantum Speed Limits

Diego Paiva Pires, Marco Cianciaruso, Lucas C. Céleri, Gerardo Adesso, Diogo O. Soares-Pinto

Published Jun 2, 2016• 265 citations
arXivHTMLPDF

Abstract

Understanding the speed with which a quantum system can evolve between distinguishable states has applications in quantum technology. A new theoretical study demonstrates a general family of quantum speed limits that can be applied to any physical process.
DOI
10.1103/physrevx.6.021031

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Quantum speed limits are relations yielding lower bounds on the evolution time of quantum systems. These results have been generalized in some ways, in particular by including evolutions to non-orthogonal states. However, there was a gap in the literature on this area, for only unitary evolutions -- closed quantum systems -- had been considered. On this Ph.D. thesis, such limitation is overcome: our main result is a bound for quantum-system evolutions in general, whether unitary or not, and correctly recovers the known bounds in the unitary case. Applications of this bound to several concrete cases of interest are herein presented. This bound is also used to extend to the non-unitary case the discussion of the role of entanglement in fast evolutions, leading to nontrivial results. For the derivation of the results, a geometric approach has been employed, which allows a clear interpretation of the bounds and a discussion of the criteria for their saturation. No previous knowledge of quantum-state geometry by the reader has been assumed.
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