We prove fundamental rigorous bounds on the speed of quantum evolution for a quantum system coupled to a thermal bath. The bounds are formulated in terms of expectation values of few-body observables derived from the system-bath Hamiltonian. They do not rely on the Markov approximation and, as a consequence, are applicable beyond the limit of weak system-bath coupling.
We prove fundamental rigorous bounds on the speed of quantum evolution for a quantum system coupled to a thermal bath. The bounds are formulated in terms of expectation values of few-body observables derived from the system-bath Hamiltonian. They do not rely on the Markov approximation and, as a consequence, are applicable beyond the limit of weak system-bath coupling.
Quantum speed limits provide upper bounds on the rate with which a quantum system can move away from its initial state. Here, we provide a different kind of speed limit, describing the divergence of a perturbed open system from its unperturbed trajectory. In the case of weak coupling, we show that the divergence speed is bounded by the quantum Fisher information under a perturbing Hamiltonian, up to an error which can be estimated from system and bath timescales. We give three applications of our speed limit. First, it enables experimental estimation of quantum Fisher information in the presence of decoherence that is not fully characterized. Second, it implies that large quantum work fluctuations are necessary for a thermal system to be driven quickly out of equilibrium under a quench. Moreover, it can be used to bound the response to perturbations of expectation values of observables in open systems.
In the Schr\"odinger picture, the state of a quantum system evolves in time and the quantum speed limit describes how fast the state of a quantum system evolves from an initial state to a final state. However, in the Heisenberg picture the observable evolves in time instead of the state vector. Therefore, it is natural to ask how fast an observable evolves in time. This can impose a fundamental bound on the evolution time of the expectation value of quantum-mechanical observables. We obtain the quantum speed limit time bound for observable for closed systems, open quantum systems, and arbitrary dynamics. Furthermore, we discuss various applications of these bounds. Our results can have several applications ranging from setting the speed limit for operator growth, correlation growth, quantum thermal machines, quantum control, and many-body physics.
Quantum speed limits are rigorous estimates on how fast a state of a quantum system can depart from the initial state in the course of quantum evolution. Most known quantum speed limits, including the celebrated Mandelstam-Tamm and Margolus-Levitin ones, are general bounds applicable to arbitrary initial states. However, when applied to mixed states of many-body systems, they, as a rule, dramatically overestimate the speed of quantum evolution and fail to provide meaningful bounds in the thermodynamic limit. Here we derive a quantum speed limit for a closed system initially prepared in a thermal state and evolving under a time-dependent Hamiltonian. This quantum speed limit exploits the structure of the thermal state and, in particular, explicitly depends on the temperature. In a broad class of many-body setups it proves to be drastically stronger than general quantum speed limits.
We investigate the bound on the speed of state transformation in the quantum systems that are coupled to general environments.We focus on the energy fluctuation of the target system and the coupling to the environment, and clarify the universal constraint on the state transformation deriving the general speed-limit inequality.This speed-limit inequality is applicable to any open systems including physical situations that have not been studied so far.We apply the inequality to the thermalization phenomena in isolated quantum systems, and the quantum cyclic engines.For the thermalization, we provide several inequalities to estimate the equilibration time.In the cyclic heat engines, we derive a rigorous constraint on the state change in the cycle where the Planck constant plays a fundamental role.
Speed of state transitions in macroscopic systems is a crucial concept for foundations of nonequilibrium statistical mechanics as well as various applications in quantum technology represented by optimal quantum control.While extensive studies have made efforts to obtain rigorous constraints on dynamical processes since Mandelstam and Tamm, speed limits that provide tight bounds for macroscopic transitions have remained elusive.Here, by employing the local conservation law of probability, the fundamental principle in physics, we develop a general framework for deriving qualitatively tighter speed limits for macroscopic systems than many conventional ones.We show for the first time that the speed of the expectation value of an observable defined on an arbitrary graph, which can describe general many-body systems, is bounded by the "gradient" of the observable, in contrast with conventional speed limits depending on the entire range of the observable.This framework enables us to derive novel quantum speed limits for macroscopic unitary dynamics.Unlike previous bounds, the speed limit decreases when the expectation value of the transition Hamiltonian increases; this intuitively describes a new trade-off relation between time and the quantum phase difference.Our bound is dependent on instantaneous quantum states and thus can achieve the equality condition, which is conceptually distinct from the Lieb-Robinson bound.We also find that, beyond expectation values of macroscopic observables, the speed of macroscopic quantum coherence can be bounded from above by our general approach.The newly obtained bounds are verified in transport phenomena in particle systems and nonequilibrium dynamics in many-body spin systems.We also demonstrate that our strategy can be applied for finding new speed limits for macroscopic transitions in stochastic systems, including quantum ones, where the bounds are expressed by the entropy production rate.Our work elucidates novel speed limits on the basis of local conservation law, providing fundamental limits to various types of nonequilibrium quantum macroscopic phenomena.
Tracking the time evolution of a quantum state allows one to verify the thermalization rate or the propagation speed of correlations in generic quantum systems. Inspired by the energy-time uncertainty principle, bounds have been demonstrated on the maximal speed at which a quantum state can change, resulting in immediate and practical tasks. Based on a programmable superconducting quantum processor, we test the dynamics of various emulated quantum mechanical systems encompassing single- and many-body states. We show that one can test the known quantum speed limits and that modifying a single Hamiltonian parameter allows the observation of the crossover of the different bounds on the dynamics. We also unveil the observation of minimal quantum speed limits in addition to more common maximal ones, i.e., the lowest rate of change of a unitarily evolved quantum state. Our results show a comprehensive experimental characterization of quantum speed limits and enhance the understanding for their subsequent study in engineered non-unitary conditions. Quantum speed limits are fundamental constraints on the speed of quantum state evolution. Here, the authors observe the known maximal quantum speed limits for few and many-body states on a superconducting quantum processor and identify the minimal quantum speed limits, which are less common than maximal ones.