The quantum speed limit (QSL) of the double quantum dot (DQD) system has been theoretically investigated by adopting the detection of the quantum point contact (QPC) in the pure dephasing environment. The Mandelstam–Tamm (MT) type of the QSL bound which is based on the trace distance has been extended to the DQD system for calculating the shortest evolving time. The increase of decoherence rate can weaken the capacity for potential speedup (CPS) and delay the evolving process due to the frequently measurement localizing the electron in the DQD system. The system needs longer time to evolve to the target state as the enhancement of dephasing rate, because the strong interaction between pure dephasing environment and the DQD system could vary the oscillation of the electron. Increasing the dephasing rate can sharp the QSL bound, but the decoherence rate would weaken the former effect and vice versa. Moreover, the CPS would be raised by increasing the energy displacement, while the enhancement of the coupling strength between two quantum dots can diminish it. It is interesting that there has an inflection point, when the coupling strength is less than the value of the point, the increasing effect of the CPS from the energy displacement is dominant, otherwise the decreasing tendency of the CPS is determined by the coupling strength and suppress the action of the energy displacement if the coupling strength is greater than the point. Our results provide theoretical reference for studying the QSL time in a semiconductor device affected by numerous factors.
The quantum speed limit (QSL) of the double quantum dot (DQD) system has been theoretically investigated by adopting the detection of the quantum point contact (QPC) in the pure dephasing environment. The Mandelstam–Tamm (MT) type of the QSL bound which is based on the trace distance has been extended to the DQD system for calculating the shortest evolving time. The increase of decoherence rate can weaken the capacity for potential speedup (CPS) and delay the evolving process due to the frequently measurement localizing the electron in the DQD system. The system needs longer time to evolve to the target state as the enhancement of dephasing rate, because the strong interaction between pure dephasing environment and the DQD system could vary the oscillation of the electron. Increasing the dephasing rate can sharp the QSL bound, but the decoherence rate would weaken the former effect and vice versa. Moreover, the CPS would be raised by increasing the energy displacement, while the enhancement of the coupling strength between two quantum dots can diminish it. It is interesting that there has an inflection point, when the coupling strength is less than the value of the point, the increasing effect of the CPS from the energy displacement is dominant, otherwise the decreasing tendency of the CPS is determined by the coupling strength and suppress the action of the energy displacement if the coupling strength is greater than the point. Our results provide theoretical reference for studying the QSL time in a semiconductor device affected by numerous factors.
We study theoretically the geometric phase of a double-quantum-dot (DQD) system measured by a quantum point contact (QPC) in the pure dephasing and dissipative environments, respectively. The results show that in these two environments, the coupling strength between the quantum dots has an enhanced impact on the geometric phase during a quasiperiod. This is due to the fact that the expansion of the width of the tunneling channel connecting the two quantum dots accelerates the oscillations of the electron between the quantum dots and makes the length of the evolution path longer. In addition, there is a notable near-zero region in the geometric phase because the stronger coupling between the system and the QPC freezes the electron in one quantum dot and the solid angle enclosed by the evolution path is approximately zero, which is associated with the quantum Zeno effect. For the pure dephasing environment, the geometric phase is suppressed as the dephasing rate increases which is caused only by the phase damping of the system. In the dissipative environment, the geometric phase is reduced with the increase of the relaxation rate which results from both the energy dissipation and phase damping of the system. Our results are helpful for using the geometric phase to construct the fault-tolerant quantum devices based on quantum dot systems in quantum information.
We theoretically study the electron transfer properties of a double quantum dot system in dissipative and pure dephasing environments based on a quantum dot contact detector. Theoretical results show that in the dissipative environment, the decoherence caused by the detector would increase the stable value of the average current and Fano factor as functions of time. Meanwhile, we find the existence of the quantum Zeno effect during the process of dynamical evolution. In the case of symmetric DQD, the relaxation caused by the dissipative environment would decrease the amplitude of the average current with time evolution and increase the value of the Fano factor in the long time limit. In the case of asymmetric DQD, the relaxation reduces the peak value of Fano factor over time. In the pure dephasing environment, we find that the frequent measurement would hinder the switch between different current channels during the cotunneling process. This results in a high value of Fano factor. In the case of symmetric DQD, increasing the pure dephasing rate would improve the value of Fano factor. In the case of asymmetric DQD, the dynamical evolution with time is not sensitive to the pure dephasing rate. In addition, it is indicated that the transfer probability of electron in the detector is only affected by the coupling between QPC and DQD. The environments have no effect on the transfer of a single electron in the detector. Our theoretical results provide theoretical references for experimental researchers to study the electron transport properties.
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.
Quantum theory sets a bound on the speed of quantum evolution. The shortest time needed for a quantm system to evolve from an initial state to the target state is known as the quantum speed limit time. The study of this time in open and closed quantum systems has been the subject of much work in quantum information theory. Quantum speed limit time is inversely related to the evolution rate of a quantum process. This relation is such that the speed of evolution decreases with increasing quantum speed limit time and vice versa. In this work we study the QSL time for the case in which a qubit interacts with a quantum critical environment. We choose the environment to be an Ising spin chain in a transverse field. It is observed that for the quantum speed limit time has a direct relation with quantum coherence of the initial state of the system. We will also study the effect of perturbation coupling on quantum speed limit time. It is observed that the quantum speed limit time decreases with increasing the coupling parameter. It is also observed that the quantum speed limit time decreases with increasing the number of spin in spin chain.
As one of the fundamental questions, quantum speed limit (QSL) is of vital role in the community of quantum physics, which sets the ultimate, maximal speed with which a quantum system can evolve. QSL originated from the understanding of the Heisenberg uncertainty relation. In 1945, Mandelstam and Tamm found the time Δt in the celebrated relation ΔEΔt≥ℏ could be thought as the minimum time that a quantum system needs to evolve from an initial state to the orthogonal state for unitary evolution. QSL sets the lower bound of the evolution. They established the relationship between the minimum evolution time ( τQSL ) and the energy uncertainty of the system (ΔE), namely τQSL=πℏ/(2ΔE) , the Mandelstam-Tamm (MT) bound. Later, Margolus and Levitin derived another different bound for a closed system which connected the τQSL with the average energy of the system ( 〈E〉 ), i.e., τQSL=πℏ/(2〈E〉) , the Margolus-Levitin (ML) bound. Combining the MT and ML bounds together, we can have a unified bound for a unitary system and orthogonal states. In the case of open system dynamics, because there is energy and/or coherence exchange between the system and the environment, the orthogonal final state of the initial state can hardly be reached any longer. An investigation of the QSL on non-unitary quantum evolution needs to be considered. The generalized QSLs are established by employing the distance between the distinguishable states. Different metrics define different distances, leading to different QSL bounds. We show a few typical generalized QSL bounds based on different metrics. And the unified QSL bound for non-unitary evolution is obtained by combining the generalized MT and ML bounds under the same metric. The generations and developments of QSL have successfully generalized the MT bounds. Even the ML bounds have been attempted to generalize, the current studies of ML bound are thought as the significantly harder task, and keep as the open questions. The influences of external environment and quantum system dynamics which include the role of entanglement in QSL for open dynamics and many-body systems, the relation between the maximum interaction speed and QSL in quantum spin systems, the non-Markovianity effect of the environment on accelerating the speed of evolution have been investigated. Furthermore, by employing the gauge invariant distance in the Riemannian metric, we establish a distinct QSL bound, which relates the quantum speed limit time to the geometry phase, and presents the geometric and gauge invariant properties of it. The bound shows the impacts of the transmission modes of the state vectors on the evolution path in the manifold. Different from the established MT and ML bounds, our bound establishes the relation between the QSL and the Pancharatnam connection 1-form, and our results show that the QSL can be controlled via manipulating the generalized Pahcharatnam connection. Also, our results of QSL are holonomy via the generalized Pahcharatnam connection, which show us a possible technique to speed up the holonomic quantum computation. The bound is also interesting to the metrology and non-equilibrium thermodynamics, etc. QSL has also been studied in the quantum representation of Wigner function. In the future research of quantum speed limit, there are many issues that need to be considered, such as the generalized ML bound, the unified QSL bound under different metrics, the application of maximum rate of quantum information derived from the QSL, and the relation between the quantum speed limit and the quantum heat engine, etc.
We study the dynamics of a double quantum dot (DQD) system interacting with a Gaussian white noise (GWN) environment which is measured by a quantum point contact (QPC) device. With both the transverse and longitudinal noise taken into account, we utilize an effective method by adding an additional Bloch vector to calculate the cumulant generating functions of the electron transfer in the QPC detector based on the full counting statistics. We study the average detector current, Fano factor, and average waiting time of the electron transfer in the presence of decoherence effects of the DQD system caused by both the QPC and the GWN environment. It indicates that the decoherence effects arising from the QPC and the GWN environment have obviously different influences on the electron transfer detected by the QPC device in both short-time and long-time limits. It is shown that the measurement process would localize the electron in a DQD in a short time and that the distribution of the average current and Fano factor versus level displacement in long-time limit are broadened due to the interaction between the system and GWN environment, which provides a reliable method to explore the dynamical behavior of an open quantum system and to extract the characteristics of the environment by analyzing the detector outcome. Our results provide theoretical support for studies of quantum measurement in a semiconductor device affected by a fluctuant environment.