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Operational definition of a quantum speed limit

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 Added by Jing Liu
 Publication date 2020
  fields Physics
and research's language is English




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The quantum speed limit is a fundamental concept in quantum mechanics, which aims at finding the minimum time scale or the maximum dynamical speed for some fixed targets. In a large number of studies in this field, the construction of valid bounds for the evolution time is always the core mission, yet the physics behind it and some fundamental questions like which states can really fulfill the target, are ignored. Understanding the physics behind the bounds is at least as important as constructing attainable bounds. Here we provide an operational approach for the definition of the quantum speed limit, which utilizes the set of states that can fulfill the target to define the speed limit. Its performances in various scenarios have been investigated. For time-independent Hamiltonians, it is inverse-proportional to the difference between the highest and lowest energies. The fact that its attainability does not require a zero ground-state energy suggests it can be used as an indicator of quantum phase transitions. For time-dependent Hamiltonians, it is shown that contrary to the results given by existing bounds, the true speed limit should be independent of the time. Moreover, in the case of spontaneous emission, we find a counterintuitive phenomenon that a lousy purity can benefit the reduction of the quantum speed limit.



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We derive a family of quantum speed limit results in time independent systems with pure states and a finite dimensional state space, by using a geometric method based on right invariant action functionals on SU(N). The method relates speed limits for implementing quantum gates to bounds on orthogonality times. We reproduce the known result of the Margolus-Levitin theorem, and a known generalisation of the Margolis-Levitin theorem, as special cases of our method, which produces a rich family of other similar speed limit formulas corresponding to positive homogeneous functions on su(n). We discuss the general relationship between speed limits for controlling a quantum state and a systems time evolution operator.
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Quantum speed limit (QSL) under noise has drawn considerable attention in real quantum computational processes and quantum communication. Though non-Markovian noise is proven to be able to accelerate quantum evolution for a damped Jaynes-Cummings model, in this work we show that non-Markovianity may even slow down the quantum evolution of an experimentally controllable photon system. As an important application, QSL time of a photon can be well controlled by regulating the relevant environment parameter properly, which is close to reach the currently available photonic experimental technology.
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