The evaluation of the minimal evolution time between two distinguishable states of a system is important for assessing the maximal speed of quantum computers and communication channels. Lower bounds for this minimal time have been proposed for unitary dynamics. Here we show that it is possible to extend this concept to nonunitary processes, using an attainable lower bound that is connected to the quantum Fisher information for time estimation. This result is used to delimit the minimal evolution time for typical noisy channels.
The evaluation of the minimal evolution time between two distinguishable states of a system is important for assessing the maximal speed of quantum computers and communication channels. Lower bounds for this minimal time have been proposed for unitary dynamics. Here we show that it is possible to extend this concept to nonunitary processes, using an attainable lower bound that is connected to the quantum Fisher information for time estimation. This result is used to delimit the minimal evolution time for typical noisy channels.
The laws of quantum physics place a limit on the speed of computation, in particular the evolution time of a system cannot be arbitrarily fast. Bounds on the speed of evolution for unitary dynamics have been long studied. A few bounds on the speed of evolution for noisy dynamics have also been obtained recently, these bounds, however, are in general not tight. In this article we present a new framework for quantum speed limit of noisy dynamics. With this framework we obtain the exact maximal angle that a noisy dynamics can achieve at any given time, this then provides tight bounds on the evolution time for noisy dynamics. The obtained bound reveals that noisy dynamics are generically different from unitary dynamics, in particular we show that the 'orthogonalization' time, which is the minimum time needed to evolve any state to its orthogonal states, is in general not applicable to noisy dynamics.
The lower bounds of the evolution time between two distinguishable states of a system, defined as quantum speed limit time, can characterize the maximal speed of quantum computers and communication channels. We study the quantum speed limit time between the composite quantum states and their target states in the presence of nondissipative decoherence. For the initial states with maximally mixed marginals, we obtain the exact expressions of the quantum speed limit time which mainly depend on the parameters of the initial states and the decoherence channels. Furthermore, by calculating the quantum speed limit time for the time-dependent states started from a class of initial states, we discover that the quantum speed limit time gradually decreases in time, and the decay rate of the quantum speed limit time would show a sudden change at a certain critical time. Interestingly, at the same critical time, the composite system dynamics would exhibit a sudden transition from classical decoherence to quantum decoherence.
The traditional quantum speed limits are not attainable for many physical processes, as they tend to be loose and fail to determine the exact time taken by quantum systems to evolve. To address this we derive exact quantum speed limits for the unitary dynamics of pure-state quantum systems that outperform the existing quantum speed limits. Using these exact quantum speed limits, we can precisely estimate the evolution time for two- and higher-dimensional quantum systems. Additionally, for both finite- and infinite-dimensional quantum systems, we derive an improved Mandelstam-Tamm bound for pure states and show that this bound always saturates for any unitary generated by self-inverse Hamiltonians. Furthermore, we show that our speed limits establish an upper bound on the quantum computational circuit complexity and yield a tighter quantum Cramér-Rao bound. These results will have a significant impact on our understanding of quantum physics as well as rapidly developing quantum technologies, such as quantum computing, quantum control, and quantum batteries.
Bounds of the minimum evolution time between two distinguishable states of a system can help to assess the maximal speed of quantum computers and communication channels. We study the quantum speed limit time of a composite quantum states in the presence of nondissipative decoherence. For the initial states with maximally mixed marginals, we obtain the exactly expressions of quantum speed limit time which mainly depend on the parameters of the initial states and the decoherence channels. Furthermore, by calculating quantum speed limit time for the time-dependent states started from a class of initial states, we discover that the quantum speed limit time gradually decreases in time, and the decay rate of the quantum speed limit time would show a sudden change at a certain critical time. Interestingly, at the same critical time, the composite system dynamics would exhibit a sudden transition from classical to quantum decoherence.
Limitations to the speed of evolution of quantum systems, typically referred to as quantum speed limits (QSLs), have important consequences for quantum control problems. However, in its standard formulation, is not straightforward to obtain meaningful QSL bounds for time-dependent Hamiltonians with unknown control parameters. In this paper we present a short introductory overview of quantum speed limit for unitary dynamics and its connection to quantum control. We then analyze potential methods for obtaining new bounds on control times inspired by the QSL. We finally extend the work in [Poggi, Lombardo and WisniackiEPL104 40005 (2013)] by studying the properties and limitations of these new bounds in the context of a driven two-level quantum system.
The quantum speed limit (QSL) is a fundamental concept in quantum mechanics, providing a lower bound on the evolution time. The attainability of the QSL, which greatly depends on the understanding of the QSL, is a long-standing open problem, especially for high-dimensional systems. In this paper, we solve this problem by establishing a QSL suitable and attainable for both open and closed quantum systems based on a new proposed state distance. It is shown that, given any initial state in a certain finite dimension, unitary and nonunitary dynamics can always be found to attain our QSL bound in the corresponding dimension, and for any given Hamiltonian for a unitary evolution a pair of states always exists, attaining the bound. As applications, we demonstrate the QSL time attained by various physical settings. This paper will shed light on the QSL problems.