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Europhysics Letters (EPL)

Machine learning study of the relationship between the geometric and entropy discord

Xiaoyu Li, Qin-Sheng Zhu, Mingzheng Zhu, Yiming Huang, Hao Wu, Shao-Yi Wu

Published Sep 3, 2019• 15 citations
Publisher

Abstract

As an important resource to realize quantum information, quantum correlation displays different behaviors, freezing phenomenon and nonlocalization, which are dissimilar to the entanglement and classical correlation, respectively. In our setup, the ordering of the value of quantum correlation is represented for different quantization methods by considering an open quantum system scenario. The machine learning method (neural network method) is then adopted to train for the construction of a bridge between the Rényi discord ( α = 2 ) and the geometric discord (Bures distance) for X form states. Our results clearly demonstrate that the machine learning method is useful for studying the differences and commonalities of different quantizing methods of quantum correlation.

DOI
10.1209/0295-5075/127/20009

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As an important resource to realize quantum information, quantum correlation displays different behaviors, freezing phenomenon and non-localization, which are dissimilar to the entanglement and classical correlation, respectively. In our setup, the ordering of quantum correlation is represented for different quantization methods by considering an open quantum system scenario. The machine learning method (neural network method) is then adopted to train for the construction of a bridge between the Rènyi discord (α=2α=2α=2) and the geometric discord (Bures distance) for XXX form states. Our results clearly demonstrate that the machine learning method is useful for studying the differences and commonalities of different quantizing methods of quantum correlation.
Quantum correlation shows a fascinating nature of quantum mechanics and plays an important role in some physics topics, especially in the field of quantum information. Quantum correlations of the composite system can be quantified by resorting to geometric or entropy methods, and all these quantification methods exhibit the peculiar freezing phenomenon. The challenge is to find the characteristics of the quantum states that generate the freezing phenomenon, rather than only study the conditions which generate this phenomenon under a certain quantum system. In essence, this is a classification problem. Machine learning has become an effective method for researchers to study classification and feature generation. In this work, we prove that the machine learning can solve the problem of X form quantum states, which is a problem of physical significance. Subsequently, we apply the density-based spatial clustering of applications with noise (DBSCAN) algorithm and the decision tree to divide quantum states into two different groups. Our goal is to classify the quantum correlations of quantum states into two classes: one is the quantum correlation with freezing phenomenon for both Rènyi discord (
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 Quantum discord characterizes non-classical correlations between two or more subsystems that persist even in the absence of entanglement. Unlike quantum entanglement, this measure captures more general quantum correlations, yet its estimation remains challenging due to the inherent difficulty in determining the optimal measurement orientations. In this work, we present a machine learning approach to estimate quantum discord for two-qubit systems with the help of artificial neural networks. Two distinct input strategies are investigated: one involving complete quantum state information derived from the density matrix elements and the other involving partial information derived from the expected values of measurements. Numerical simulations demonstrate that both artificial neural network architectures can predict the quantum discord of new quantum states with high precision. Our findings provide a new way to estimate quantum correlations, demonstrating the effectiveness of machine learning in quantum information tasks.
Quantum correlations represent a fundamental tool for studies ranging from basic science to quantum technologies. Different non-classical correlations have been identified and studied, as entanglement and discord. In this Paper we explore experimentally the rich geometry of polarization Bell-diagonal states. By taking advantage of the statistical method of generation, the values of entanglement and discord along different trajectories in the space of the parameters of density matrix have been measured. The effects of sudden death of entanglement and complete "freeze" of discord were investigated in order to detect the domains with different domination of one type of quantum correlation against to other. A geometric interpretation for each considered phenomena is addressed. The observed good agreement between experiment and theory for all investigated trajectories ensures the reliability of this method.