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Acta Physica Sinica

Effects of ambient noise on quantum speed limit time and quantum discord dynamics of a double “gravitational cat state” system

Youcheng DAI, Wei Han, Ying-Jie Zhang

Published Dec 25, 2024• 0 citations
Publisher

Abstract

The exploration of the quantum nature of gravity has always been the focus of academic research. In this work, we consider a double “gravitational cat state” quantum system consisting of a pair of massive particles coupled with gravitational interaction confined in their respective double potential wells. Specifically, we model the double “gravitational cat state” system as a two-qubit system by assuming that the system is initially in the two-qubit Bell state, and investigate the effects of stable classical field and decayed field noise on the quantum speed limit time (QSLT) and trace distance discord (TDD) dynamics of the double “gravitational cat state”. The results show that the QSLT can be controlled by changing the parameters of the system and the environment, and the quantum state dynamic evolution of the system with massive particles can be accelerated. The quantum state evolution can be accelerated by increasing the gravitational coupling intensity between the two massive particles. The decay rate of the decaying field can also regulate the QSLT of the system to a certain extent, so as to accelerate the quantum state evolution. Under the influence of decaying field noise, it is worth noting that the intensity of gravitational coupling affects the frequency of quantum discord oscillations in this two-particle system. The QSLT shows an oscillating trend with time: rapidly increasing to a certain value in a short period of time, then beginning to decline, and then oscillating until it reaches a stable value. That is to say, the evolution of quantum states goes through an oscillatory cycle of first deceleration and then acceleration until the evolution rate becomes stable after a certain period of time. At the same time, there are similar oscillations in the dynamics of quantum discord. Moreover, by comparing these two, it is found that the QSLT decreases in the process of increasing the quantum discord in the system. When the discord oscillation has regularity, the QSLT tends to a certain value, and the quantum discord of the double “gravitational cat state” system has a certain relationship with the QSLT. In other words, the quantum discord will affect the rate of quantum state evolution to some extent, and the increase of quantum discord between systems will be more conducive to the evolution of quantum states.

DOI
10.7498/aps.74.20241514

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The exploration of the quantum nature of gravity has always been the focus of academic research. In this work, we consider a double “gravitational cat state” quantum system consisting of a pair of massive particles coupled with gravitational interaction confined in their respective double potential wells. Specifically, we model the double “gravitational cat state” system as a two-qubit system by assuming that the system is initially in the two-qubit Bell state, and investigate the effects of stable classical field and decayed field noise on the quantum speed limit time (QSLT) and trace distance discord (TDD) dynamics of the double “gravitational cat state”. The results show that the QSLT can be controlled by changing the parameters of the system and the environment, and the quantum state dynamic evolution of the system with massive particles can be accelerated. The quantum state evolution can be accelerated by increasing the gravitational coupling intensity between the two massive particles. The decay rate of the decaying field can also regulate the QSLT of the system to a certain extent, so as to accelerate the quantum state evolution. Under the influence of decaying field noise, it is worth noting that the intensity of gravitational coupling affects the frequency of quantum discord oscillations in this two-particle system. The QSLT shows an oscillating trend with time: rapidly increasing to a certain value in a short period of time, then beginning to decline, and then oscillating until it reaches a stable value. That is to say, the evolution of quantum states goes through an oscillatory cycle of first deceleration and then acceleration until the evolution rate becomes stable after a certain period of time. At the same time, there are similar oscillations in the dynamics of quantum discord. Moreover, by comparing these two, it is found that the QSLT decreases in the process of increasing the quantum discord in the system. When the discord oscillation has regularity, the QSLT tends to a certain value, and the quantum discord of the double “gravitational cat state” system has a certain relationship with the QSLT. In other words, the quantum discord will affect the rate of quantum state evolution to some extent, and the increase of quantum discord between systems will be more conducive to the evolution of quantum states.
We derive Margolus-Levitin and Mandelstamm-Tamm type bound on the quantum speed limit time for the creation and decay of quantum correlations by an amount in a quantum system evolving under the influence of its ambient environment. The minimum distance of a non-classical state from an appropriate set of classical states is a legitimate measure of the quantumness of the state. We consider entanglement and quantum discord measures of quantum correlations, quantified using the Bures distance-based measure. To demonstrate the impact of quantum noise on this speed limit time for quantum correlations, we estimate the quantum speed limit time for the creation and decay of quantum correlations for a two-qubit system under modified OUN dephasing and collective two-qubit decoherence channels.
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.
In this paper, we investigate the time evolution of quantum correlations in a two-qubit system influenced by an optical channel. The system?s dynamics are analyzed in terms of concurrence (CN), Bell non-locality (BN), and trace distance discord (TDD), which quantify entanglement, non-local correlations, and quantum discord, respectively. Our model explores the impact of key parameters such as the beam-splitter angle, ?, channel parameter, ?, and angular frequency, ?, on these quantum correlations. The results show that CN and BN exhibit oscillatory behavior with periodic revivals, but tend to decay more rapidly under noisy conditions. Conversely, TDD demonstrates greater robustness, persisting even when CN and BN collapse, indicating the survival of quantum correlations in separable states. Higher noise strength and angular frequencies induce faster oscillations and revivals across all measures, with systems prepared with stronger initial quantum correlations showing increased resilience. This study highlights the robustness of quantum discord in noisy environments and its potential role in quantum information processing, even in the absence of entanglement.
Abstract Using quantum discord (QD) and geometric quantum discord (GQD), quantum correlation dynamics is investigated for two coupled qubits within a multiqubit interacting system in the zero-temperature bosonic reservoir, under both weak and strong qubit-reservoir coupling regimes. The multiqubit system is connected with either a common bosonic reservoir (CBR) or multiple independent bosonic reservoirs (IBRs). In the CBR case, our findings indicate that both QD and GQD can be strengthened by increasing the number of qubits in the multiqubit system. Furthermore, we study the steady state QD and GQD in the strong coupling regime, and find that the stable value in the long-time limit is determined exclusively by the number of qubits. The evolution period of QD and GQD gets longer as the dipole–dipole interaction (DDI) strength increases, which helps prolong the correlation time and thus preserves the quantum correlation under the weak coupling regime. Further analysis reveals notable differences between the CBR and IBRs scenarios. In the IBRs case, the decay of QD and GQD becomes slower compared to the CBR case, with both measures tending to zero at a reduced rate. Moreover, GQD consistently exhibits lower values than QD in both scenarios. These findings provide valuable insights into the selection of appropriate correlation measurement techniques for quantifying quantum correlations.
We study the quantum discord dynamics of two noninteracting qubits that are, respectively, subject to classical noise. The results show that the dynamics of quantum discord are dependent on both the coupling between the qubits and classical noise, and the average switching rate of the classical noise. In the weak-coupling Markovian region, quantum discord exhibits exponent decay without revival, and can be well protected by increasing the average classical noise switching rate. While in the strong-coupling non-Markovian region, quantum discord reveals slowly decayed oscillations with quick revival by decreasing the average switching rate of the classical noise. Thus, our results provide a new method of protecting quantum discord in a two-qubit system by controlling the coupling between the qubits and classical noise, and the average switching rate of the classical noise.
Abstract We illustrate two linear configurations (one-side model and two-side model) for implementing a non-Markovian speedup evolution of a massive particle gravitationally coupled with a controllable environment: multiple massive particles. By controlling the environment, for instance by choosing a judicious the mass of the environmental particles or by changing the separation distance of each massive particle, two dynamical crossover behaviors from Markovian to non-Markovian and from no-speedup to speedup are achieved due to the gravitational interactions between the system particle and each environmental particle. Numerical calculation also shows that the critical mass of the environmental particles or the critical separation distance for these two dynamical crossover behaviors restrict each other directly. The larger the value of the mass of the environmental particles is, the smaller the value of the critical separation distance should be requested. In this work, the non-Markovian dynamics is the principal physical reason for the speedup evolution of a quantum system. Particularly, the non-Markovianity of the system mass particle in the two-side model has better correspondence with the quantum speed limit time than that in the one-side model.