We theoretically study the quantum speed limits (QSLs) of a qubit system coupled to a thermal dephasing environment with an Ohmic-like spectral density. Based on the geometric QSLs time bound, which is derived by employing the trace distance to quantify the geodesic between two distinguishable states in dynamical evolution, we study the influences of the temperature and spectral density of the environment on the QSLs time of the dephasing qubit. We also investigate the interplay between the QSLs time, the environmental temperature, and the spectral density of the environment. It has been demonstrated that the QSLs time closely depends on the transition frequency and the dynamical behavior (e.g., coherence trapping) of the dephasing qubit. For a fixed Ohmicity parameter of the environmental spectral density, the increase in environmental temperature can enhance the QSLs time bound. In addition, when the environmental temperature remains constant, the increase in the Ohmicity parameter initially leads to a reduction in the QSLs time bound, which is then followed by an increase in the time bound of QSLs. Our results can help to better understand the QSLs in the dynamics of open quantum systems and have potential application in the modulation of QSLs time in the dephasing qubit by engineering the spectral density of the environment.
We theoretically study the quantum speed limits (QSLs) of a qubit system coupled to a thermal dephasing environment with an Ohmic-like spectral density. Based on the geometric QSLs time bound, which is derived by employing the trace distance to quantify the geodesic between two distinguishable states in dynamical evolution, we study the influences of the temperature and spectral density of the environment on the QSLs time of the dephasing qubit. We also investigate the interplay between the QSLs time, the environmental temperature, and the spectral density of the environment. It has been demonstrated that the QSLs time closely depends on the transition frequency and the dynamical behavior (e.g., coherence trapping) of the dephasing qubit. For a fixed Ohmicity parameter of the environmental spectral density, the increase in environmental temperature can enhance the QSLs time bound. In addition, when the environmental temperature remains constant, the increase in the Ohmicity parameter initially leads to a reduction in the QSLs time bound, which is then followed by an increase in the time bound of QSLs. Our results can help to better understand the QSLs in the dynamics of open quantum systems and have potential application in the modulation of QSLs time in the dephasing qubit by engineering the spectral density of the environment.
We develop an intuitive geometric picture of quantum states, define a particular state distance, and derive a quantum speed limit (QSL) for open systems. Our QSL is attainable because any initial state can be driven to a final state by the particular dynamics along the geodesic. We present the general condition for dynamics along the geodesic for our QSL. As evidence, we consider the generalized amplitude damping dynamics and the dephasing dynamics to demonstrate the attainability. In addition, we also compare our QSL with others by strict analytic processes as well as numerical illustrations, and show our QSL is tight in many cases. It indicates that our paper is significant in tightening the bound of evolution time.
Quantum speed limits (QSLs) constrain the minimum time for quantum state evolution, typically derived from energy bounds like the Margolus-Levitin (ML) and Mandelstam-Tamm (MT) relations. In open systems, decoherence—driven by environmental interactions—may impose additional constraints. This work investigates whether decoherence times fundamentally limit QSLs in spin-chain systems, extending ML/MT bounds to open dynamics. By modeling spin chains with Lindblad equations and simulating Heisenberg-type interactions, we analyze the interplay between energy fluctuations, decoherence rates, and evolution times. Experimental validation via trapped-ion or superconducting-qubit arrays could test energy-time uncertainty in many-body systems. Results suggest decoherence times establish a lower QSL bound proportional to [to verify], offering a platform to probe open-system quantum dynamics. ## 1. Introduction Quantum speed limits (QSLs) define the fastest possible evolution between distinguishable quantum states, critical for quantum computing and information processing. Closed-system QSLs, such as the ML [arXiv:quant-ph/9804014] and MT [DOI:10.1103/PhysRev.41.1019] bounds, rely on energy constraints. However, open systems—subject to decoherence—require extended frameworks. Decoherence times, governed by environmental couplings, may impose additional QSLs, yet their interplay with ML/MT bounds remains unexplored. Spin chains, realizable in trapped ions [DOI:10.1038/s41586-019-1394-6] and superconducting circuits, offer a many-body testbed for studying these effects. This work bridges open-system dynamics with QSL theory, assessing whether decoherence times set a fundamental lower bound and enabling experimental verification of energy-time uncertainty. ## 2. Background The ML bound states that a quantum system requires at least $ t_{\text{QSL}} \geq \hbar / (2\Delta E) $, where $ \Delta E $ is the energy spread. The MT bound $ t_{\text{QSL}} \geq \hbar / (2E) $, with $
Quantum state change can not occurs instantly, but the speed of quantum evolution is limited to an upper bound value, called quantum speed limit (QSL). Engineering QSL is an important task for quantum information and computation science and technologies. This paper devotes to engineering QSL and quantum correlation in simple two-qubit system suffering dephasing via Periodic Dynamical Decoupling (PDD) method in both Markovian and non-Markovian dynamical regimes. The results show that when decoupling pulses are applied to both qubits this method removes all undesirable effects of the dephasing process, completely. Applying the PDD on only one of the qubits also works but with lower efficiency. Additionally, ultra-high speedup of the quantum processes become possible during the pulse application period, for enough large number of pulses. The results is useful for high speed quantum gate implementation application.
Quantum state change cannot occur instantly, but the speed of quantum evolution is limited to an upper bound value, called quantum speed limit (QSL). Understanding the quantum speed limit time (QSLT) is fundamental to advancing the control and optimization of quantum systems under decoherence. While significant progress has been made for single-qubit systems, the dynamics of two-qubit systems remain less explored. Studying the effects of dynamical decoupling (DD), such as periodic dynamical decoupling (PDD), on QSLT in two-qubit systems provides an opportunity to explore how to approach coherence preservation, entanglement stabilization, and environmental noise suppression. This exploration can lead to optimized strategies for controlling the evolution of two-qubit systems, which serve as the foundation of quantum gates and scalable quantum architectures. By analyzing QSLT in two-qubit systems, this research seeks to find how DD techniques can be adapted to mitigate the adverse effects of decoherence and extend their coherence times. The insights from this work will also shed light on the role of non-Markovian effects in two-qubit systems, offering potential pathways for leveraging such phenomena to maintain quantum coherence. The results reveal that under special conditions when decoupling pulses are applied to both qubits, the PDD method can completely remove all undesirable effects of the pure dephasing process. Eventually, these findings try to bridge the gap between theoretical frameworks and practical applications in quantum technologies, aiming to develop high-performance quantum processors.
We investigate the quantum sensing performance of a dephasing qubit as a probe in Ohmic environments, characterized by the coupling strength η, the Ohmicity parameter s, and the cutoff frequency ωc to be estimated. The performance is quantified by the dimensionless quantum signal-to-noise ratio Q. We show that the evolution of Q with the scaled time ωct is independent of ωc, and peaks at an optimal time topt, yielding optimal sensitivity Qopt. We analyze how Qopt depends on η, s and the temperature T. Our results demonstrate that, for any Ohmic environment, provided that ωctopt≪1, Qopt always reaches the upper bound: Qmax=0.648 at zero temperature, and consistently attains Qmax/4 at high temperatures. Remarkably, we find that increasing the scaled temperature T/ωc can enhance Qopt by nearly two orders of magnitude compared to its zero-temperature counterpart for certain Ohmic environments. Our work reveals that temperature can serve as a resource to enhance sensing precision, as it accelerates the encoding of the cutoff frequency information into the probe state, thereby enabling optimal measurement within a short time window.
Abstract The quantum speed limit (QSL) is a fundamental lower bound on the evolution time for quantum systems, and its tightness has been observed to be dependent on the properties of the physical process. However, experimental studies exploring the QSL in open quantum systems are still missing. Here, we studied geometric quantum speed limits of a qubit subject to decoherence in an ensemble of chloroform molecules in a Nuclear Magnetic Resonance experiment. We controlled the system-reservoir interaction and the spin relaxation rates by adding a paramagnetic salt, allowing the observation of both Markovian and non-Markovian open system dynamics for the qubit. We used two distinguishability measures of quantum states to assess the speed of the qubit evolution: the quantum Fisher information (QFI) and Wigner-Yanase skew information (WY). For non-Markovianity and low salt concentrations, we found crossovers between QSLs related to those metrics. The WY metric sets the tighter QSL for high concentrations and Markovian dynamics. We also show that QSLs are sensitive even to small fluctuations in spin magnetization.