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  • Comment on "Geometric derivation of the quantum speed limit"

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    Author(s)
    Zwierz, Marcin
    Griffith University Author(s)
    Zwierz, Marcin
    Year published
    2012
    Metadata
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    Abstract
    Recently, Jones and Kok [Jones and Kok, Phys. Rev. A 82, 022107 (2010)] presented alternative geometric derivations of the Mandelstam-Tamm [Mandelstam and Tamm, J. Phys. (USSR) 9, 249 (1945)] and Margolus- Levitin [Margolus and Levitin, Phys. D 120, 188 (1998)] inequalities for the quantum speed of dynamical evolution. The Margolus-Levitin inequality followed from an upper bound on the rate of change of the statistical distance between two arbitrary pure quantum states. We show that the derivation of this bound is incorrect. Subsequently, we provide two upper bounds on the rate of change of the statistical distance, expressed ...
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    Recently, Jones and Kok [Jones and Kok, Phys. Rev. A 82, 022107 (2010)] presented alternative geometric derivations of the Mandelstam-Tamm [Mandelstam and Tamm, J. Phys. (USSR) 9, 249 (1945)] and Margolus- Levitin [Margolus and Levitin, Phys. D 120, 188 (1998)] inequalities for the quantum speed of dynamical evolution. The Margolus-Levitin inequality followed from an upper bound on the rate of change of the statistical distance between two arbitrary pure quantum states. We show that the derivation of this bound is incorrect. Subsequently, we provide two upper bounds on the rate of change of the statistical distance, expressed in terms of the standard deviation of the generator K and its expectation value above the ground state. The bounds lead to the Mandelstam-Tamm inequality and a quantum speed limit which is only slightly weaker than the Margolus-Levitin inequality.
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    Journal Title
    Physical Review A
    Volume
    86
    Issue
    1
    DOI
    https://doi.org/10.1103/PhysRevA.86.016101
    Copyright Statement
    © 2012 American Physical Society. This is the author-manuscript version of this paper. Reproduced in accordance with the copyright policy of the publisher. Please refer to the journal's website for access to the definitive, published version.
    Subject
    Quantum Information, Computation and Communication
    Mathematical Sciences
    Physical Sciences
    Chemical Sciences
    Publication URI
    http://hdl.handle.net/10072/48981
    Collection
    • Journal articles

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