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Register a new userA Geometrical Derivation of a Family of Quantum Speed Limit Results
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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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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.
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.
A remarkable feature of quantum many-body systems is the orthogonality catastrophe which describes their extensively growing sensitivity to local perturbations and plays an important role in condensed matter physics. Here we show that the dynamics of the orthogonality catastrophe can be fully characterized by the quantum speed limit and, more specifically, that any quenched quantum many-body system whose variance in ground state energy scales with the system size exhibits the orthogonality catastrophe. Our rigorous findings are demonstrated by two paradigmatic classes of many-body systems -- the trapped Fermi gas and the long-range interacting Lipkin-Meshkov-Glick spin model.
Quantum speed limit, furnishing a lower bound on the required time for the evolution of a quantum system through the state space, imposes an ultimate natural limitation to the dynamics of physical devices. Quantum absorption refrigerators, on the other hand, have attracted a great deal of attention in the last few years. In this article, we discuss the effects of quantum speed limit on the performance of a quantum absorption refrigerator. In particular, we show that there exists a trade-off relation between the steady cooling rate of the refrigerator and the minimum time taken to reach the steady state. Based on this, we define a figure of merit called bounding second order cooling rate and show that this scales linearly with the unitary interaction strength among the constituent qubits. We also study the increase of bounding second order cooling rate with the thermalization strength. We subsequently demonstrate that coherence in the initial three qubit system can significantly increase the bounding second order cooling rate. We study the efficiency of the refrigerator at maximum bounding second order cooling rate and, in a limiting case, we show that the efficiency at maximum bounding second order cooling rate is given by a simple formula reminiscent of the Curzon-Ahlborn relation.
Spin chains have long been considered as candidates for quantum channels to facilitate quantum communication. We consider the transfer of a single excitation along a spin-1/2 chain governed by Heisenberg-type interactions. We build on the work of Balachandran and Gong [1], and show that by applying optimal control to an external parabolic magnetic field, one can drastically increase the propagation rate by two orders of magnitude. In particular, we show that the theoretical maximum propagation rate can be reached, where the propagation of the excitation takes the form of a dispersed wave. We conclude that optimal control is not only a useful tool for experimental application, but also for theoretical enquiry into the physical limits and dynamics of many-body quantum systems.
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