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

Researching the Link Between the Geometric and R鑞yi Discord for Special Canonical Initial States Based on Neural Network Method

Xiaoyu Li, Qin-Sheng Zhu, Qingyu Meng, Caishu You, Mingzheng Zhu, Yong Hu, Yiming Huang, Hao Wu, Desheng Zheng

Published Jan 1, 2019• 10 citations
Publisher

Abstract

Quantum correlation which is different to the entanglement and classical correlation plays important role in quantum information field. In our setup, neural network method is adopted to simulate the link between the Rènyi di... | Find, read and cite all the research you need on Tech Science Press
DOI
10.32604/cmc.2019.06060

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•Jan 1, 2013•1 citation
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.
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.
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 entanglement plays a key role in quantum information and quantum computation and thus attracts much attention in many branches of physics both in theory and in experiment. But recent studies revealed that some separable states (non-entangled state) may speed up certain tasks over their classical counterparts and may also possess certain kinds of quantum correlations. For example, geometric quantum discord, which is a more general quantum correlation measure than entanglement, can be nonzero for some separable states. From a practical point of view, it is proposed that the geometric quantum discord be responsible for the power of many quantum information processing tasks. In order to capture such correlations, Ollivier and Zurek introduced quantum discord, which measures the discrepancy between two natural yet different quantum analogues of two classically equivalent expressions of mutual information. However, the calculation of quantum discord is based on numerical maximization procedure, and there are few analytical expressions even for a two-qubit state. In order to obtain the analytical results of quantum discord, a geometric measure of quantum discord which measures the quantum correlations through the minimum Hilbert-Schmidt distance between the given state and zero discord state is introduced. Geometric quantum discord is defined as an effective measure of quantum correlation, and the geometric quantum discord through the minimal distance between the quantum state and the set of zero-discord states in a bipartite quantum system can be worked out. In this paper, by using the geometric quantum discord measurement method, the geometric quantum discord in Tavis-Cummings model is investigated, and the influences of the initial state purity, entanglement degree, dipole-dipole coupling intensity between two atoms, and field in the Fock state on the evolution characteristic of geometric quantum discord are analyzed. The results show that the geometric quantum discord appears periodically. It initially decreases to a minimum value, and then turns out to be increased for different initial states. The rigorous analysis and numerical results reveal that when we take a suitable initial state, the geometric quantum discord of two atoms can be kept in correlation. When the atoms are in the different initial states, the quantum properties of the system are significant. The photon number of the field can lead the quantum discord to be weakened. Geometric quantum discord can be increased by increasing the cavity photon number and the dipole-dipole coupling intensity. Geometric quantum discord can be enhanced obviously by increasing the strength of the dipole-dipole coupling interaction. The conclusions may conduce to the understanding of quantum correlation for the other systems from the view of geometric quantum discord.
Quantum entanglement is the most popular kind of quantum correlations. Its role in several tasks in quantum information theory like quantum cryptography, quantum dense coding and quantum teleportation is indisputable. The role of entanglement in quantum algorithms has also attracted enormous amount of attention in the literature. The research in this direction is motivated by the finding that a quantum computer can efficiently factorize arbitrary integer numbers. Since no classical algorithm is known today that can solve this problem efficiently, this example clearly demonstrates the superiority of a quantum computer compared to its classical counterpart. In this context, entanglement also plays a crucial role: if the quantum computer operates on a pure state without entanglement, then the computational process can be simulated efficiently on a classical computer. In this case entanglement is the key ingredient that makes the difference between a quantum and a classical computer. However, the situation is more involved if the computational process is not perfect. In this case the quantum computer operates on a mixed state, and the role of entanglement is less obvious. A seminal result in this direction is a quantum algorithm known under the acronym DQC1. This algorithm operates on an almost maximally mixed state with vanishingly little entanglement. However, DQC1 can still perform tasks efficiently for which no efficient classical algorithm is known today. Thus, it is reasonable to assume that entanglement in general is not related to the efficiency of a quantum algorithm. Triggered by this observation other kinds of quantum correlations have been studied. In this context a particular measure of quantum correlations known as quantum discord is referred to frequently in the literature. Quantum discord is a measure of quantum correlations beyond entanglement, i.e., a quantum state can have no entanglement, but nonvanishing quantum discord. Quantum discord is also regarded as the key resource in the DQC1 algorithm. Although this statement is still controversial, it was shown under very general assumptions that quantum discord is required if a quantum computer is to show an exponential speedup over any classical algorithm. In this thesis we give a short introduction into the theory of entanglement and general quantum correlations, and further discuss our results. In particular, we show that two different kinds of entanglement measures can coincide. This result is used to build an algorithm for computing entanglement. We also consider the role of quantum correlations for the distribution of entanglement and for the quantum measurement process. We further discuss the behavior of quantum correlations under local noise, and their monogamy properties.