Abstract
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.
Highlights
Coherence and entanglement are important resources in quantum technology, especially in quantum information processing, quantum computation [1], and quantum metrology [2,3]
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
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
Summary
Coherence and entanglement are important resources in quantum technology, especially in quantum information processing, quantum computation [1], and quantum metrology [2,3]. The most well-known scenario for the QSL is to evolve a pure state to its orthogonal state In this case, the first bound for evolution time is τMT = π /(2 H ), where. F f t=heTBrure√sρa0nρg1le√, ρas0 well as the target angle, is the fidelity between two quantum states ρ0 and ρ1 Another well-used method for the construction of the QSL is the geometric approach, which utilizes the metrics. In the case of a noncontrolled fixed Hamiltonian, the trajectory of evolution in state space is fixed for a fixed decoherence mode and strength, whether the Hamiltonian is time dependent or not This is due to the fact that the solution of states in a fixed differential equation is unique.
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