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Computers, materials & continua/Computers, materials & continua (Print)

The Controllability of Quantum Correlation Under Geometry and Entropy Discords

Xiaoyu Li, Yiming Huang, Qin-Sheng Zhu, Xusheng Liu, Desheng Zheng

Published Jan 1, 2021• 0 citations
Publisher

Abstract

Quantum correlation plays a critical role in the maintenance of quantum information processing and nanometer device design. In the past two decades, several quantitative methods had been proposed to study the quantum correlation of certain open quantum systems, including the geometry and entropy style discord methods. However, there are differences among these quantification methods, which promote a deep understanding of the quantum correlation. In this paper, a novel time-dependent three environmental open system model is established to study the quantum correlation. This system model interacts with two independent spin-environments (two spin-environments are connected to the other spin-environment) respectively. We have calculated and compared the changing properties of the quantum correlation under three kinds of geometry and two entropy discords, especially for the freezing phenomenon. At the same time, some original and novel changing behaviors of the quantum correlation under different time-dependent parameters are studied, which is helpful to achieve the optimal revival of the quantum discord and the similar serrated form of the freezing phenomenon. Finally, it shows the controllability of the freezing correlation and the robustness of these methods by adjusting time-dependent parameters. This work provides a new way to control the quantum correlation and design nanospintronic devices.

DOI
10.32604/cmc.2021.012698

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Quantum correlation plays a critical role in the maintenance of quantum information processing and nanometer device design. In the past two decades, several quantitative methods had been proposed to study the quantum correlation of certain open quantum systems, including the geometry and entropy style discord methods. However, there are differences among these quantification methods, which promote a deep understanding of the quantum correlation. In this paper, a novel time-dependent three environmental open system model is established to study the quantum correlation. This system model interacts with two independent spin-environments (two spin-environments are connected to the other spin-environment) respectively. We have calculated and compared the changing properties of the quantum correlation under three kinds of geometry and two entropy discords, especially for the freezing phenomenon. At the same time, some original and novel changing behaviors of the quantum correlation under different time-dependent parameters are studied, which is helpful to achieve the optimal revival of the quantum discord and the similar serrated form of the freezing phenomenon. Finally, it shows the controllability of the freezing correlation and the robustness of these methods by adjusting time-dependent parameters. This work provides a new way to control the quantum correlation and design nanospintronic devices.
Abstract A two qubits system interacting with two independent spin‐environments connecting with the third environment is constructed in order to demonstrate the effect of the multi‐environment for quantum correlation. In this process, the freezing phenomenon appears for SCI and X states under Quantum Discord and Geometric Discord measures, respectively, but not for the same initial state measured by different measures. Meanwhile, the properties of the freezing platform, characterized by the collapse, revival and persistent time, are researched by the different parameters. The result of this paper may pave a way to control quantum correlation and design nanospintronic devices.
Recent work has relatively comprehensively studied the quantum discord, which is supposed to account for all the nonclassical correlations present in a bipartite state (including entanglement), and provide computational speedup and quantum enhancement even in separable states. Firstly, we introduce several different indicators of nonclassical correlations, including their definitions and interpretations, mathematical properties, and the relationship between them. Secondly, we review two major topics of quantum discord. One is the remarkable behavior at quantum phase transitions. The pairwise quantum discord for nearest neighbors as well as distant spin pairs can perfectly signal the critical behavior of many physical models, even at finite temperatures. The other is quantum discord dynamics in open systems, especially for "system-spin environment" models. Quantum discord is more robust than entanglement against external perturbations. It can be created, greatly amplified or protected under certain conditions, and presents promising applications in quantum technologies such as quantum computers.
Several measures of geometric discords have been recently proposed and mostly characterized in qubits. In this work, the dynamics of four measures of geometric discords is studied for two kinds of initial states in the two-qutrit model under environments. It is shown that four indicators can display freezing in Markovian regime and multiple freezing with multiple sudden changes in non-Markovian regime for suitable initial states and model parameters. Moreover, those measures evolve in a similar manner, but they differ from the decaying or increasing rate, the oscillatory amplitude and the time interval of freezing. However, they do not exhibit any freezing for the general Bell states. The dynamical hierarchy is discussed for those indicators. Those are helpful to understand the rich phenomena of discordant dynamics in open qutrits.
Quantum information processing (QIP) based on high-dimensional quantum systems provides unique advantages and new potentials where high-dimensional quantum correlations (QCs) play vital roles. Exploring the resistance of QCs against noises is crucial as QCs are fragile due to complex and unavoidable system-environment interactions. In this study, we investigate the performance of high-dimensional QCs under local dephasing noise using a single nitrogen-vacancy center in diamond. A freezing phenomenon in the high-dimensional quantum discord dynamics was observed, showing that discord is robust against local dephasing noise. Utilizing a robustness metric known as the freezing index, we find that the discord of qutrits outperforms their qubit counterparts when confronted with dephasing noise. Furthermore, we develop a geometric picture to explain this intriguing freezing phenomenon. Our findings highlight the potential of utilizing discord as a physical resource for advancing QIP in high-dimensional quantum settings.
Super-quantum discord (SQD) with weak measurement is regarded as a kind of quantum correlation in quantum information processing. We compare and analyze the dynamical evolutions of SQD, quantum discord (QD), and quantum entanglement (QE) between two qubits in the correlated dephasing environmental model. The results indicate that (i) owing to the much smaller influence of weak measurement on the coherence of the system than that of von Neumann projection measurement, SQD with weak measurement is larger than QD, and (ii) dynamical evolution of QD or QE monotonically goes to zero with time, while SQD monotonically tends to a stable value and a freezing phenomenon occurs. The stable value after freezing mainly depends on the measurement strength and the purity of the initial quantum state.