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Malaysian Journal of Science Health & Technology

Quantum Entanglement and Its Classification Protocols

Amirul Asyraf Zhahir, Siti Munirah Mohd, Mohd Sham Mohamad, Mohd Ilias M Shuhud, Bahari Idrus, Hishamuddin B Zainuddin, Nurhidaya Mohamad Jan

Published Oct 8, 2024• 0 citations
Publisher

Abstract

Quantum entanglement has its own major role in quantum information theory. Its application in numerous areas namely quantum computing, quantum cryptography and quantum teleportation are proven vital and essential. Over the last decades, the interests in quantum entanglement have grown and significant progress in quantum computing has been revealed. However, the classification of entanglement was proved to be challenging especially in a higher qubit-dimensional system setting. In this review, indexed literature as the secondary resource was chosen by specific keywords from several database. In reference to the literatures review, there exists several entanglement classifications protocols that will be presented in this paper namely local unitary (LU), local operations and classical communication (LOCC), and stochastic local operations and classical communication (SLOCC). This study will offer a better understanding of quantum entanglement and the entanglement classification protocols.

DOI
10.33102/mjosht.v10i2.408

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Quantum entanglement has its own major role in quantum information theory. Its application in numerous areas namely quantum computing, quantum cryptography and quantum teleportation are proven vital and essential. Over the last decades, the interests in quantum entanglement have grown and significant progress in quantum computing has been revealed. However, the classification of entanglement was proved to be challenging especially in a higher qubit-dimensional system setting. In this review, indexed literature as the secondary resource was chosen by specific keywords from several database. In reference to the literatures review, there exists several entanglement classifications protocols that will be presented in this paper namely local unitary (LU), local operations and classical communication (LOCC), and stochastic local operations and classical communication (SLOCC). This study will offer a better understanding of quantum entanglement and the entanglement classification protocols.
Quantum entanglement is one of the essences of quantum mechanics and quantum information theory. It is a physical phenomenon in which entangled particles remain correlated with each other regardless of the distance between them. Quantum entanglement plays a significant role in areas such as quantum computing, quantum cryptography, and quantum teleportation. Quantifying entanglement is important for determining the depth of the entanglement level and has an impact on quantum information tasks performance. Entanglement classification is critical in quantum information theory for determining the class of states in a quantum system. The entanglement classification of two qubits as separable or entangled has been established. The classification of multiqubit entanglement is more challenging, especially in higher-qubit systems. The goal of this study is to identify different established measurements for entanglement quantification and entanglement classification methods through a systematic literature review. Indexed articles between 2017 and 2021 were selected as secondary resources from several sources based on specific keywords. This study presents a conceptual framework of entanglement quantification and classification based on previous studies.
Chapter 14 transitions the focus to multipartite entanglement, a realm that broadens the discussion from bipartite systems to those involving multiple parties. This complex form of entanglement plays a crucial role in quantum computing, cryptography, and communication networks. The chapter introduces the foundational concepts of multipartite entanglement, including its characterization and the challenges associated with its classification. Significant attention is given to the classification of multipartite entangled states through SL-invariant polynomials, which provide tools for understanding the structure and properties of these states. Stochastic Local Operations and Classical Communication (SLOCC) are introduced as a means to classify entanglement. Furthermore, the chapter explores the entanglement of assistance and the monogamy of entanglement, two concepts that illustrate the limitations and potential for distributing entanglement among multiple parties. Through detailed explanations and examples in three and four qubits, this chapter offers insights into the intricate world of multipartite entanglement, revealing both its potential and challenges.
Quantum computing is different from classical computing. It is based on quantum mechanics principles, utilizing the attributes such as entanglement and superposition. The significant difference between a quantum computer and a classical computer is the ability to process information astonishingly faster. This is possible due to the quantum entanglement concept. Interests in the quantum entanglement concept have been exponentially growing over the years. In the last decade, significant progress in implementations of quantum computation in quantum information has been achieved. This study selected secondary resource indexed literature from several databases with specific keywords in almost a century. In this paper, quantum computing and its application is presented along with the essence of quantum entanglement role in quantum computing. This study will provide a general understanding of quantum computing and its application and quantum entanglement.
Quantum entanglement is a critical physical process in quantum mechanics and quantum information theory. It is a required process in quantum computing, quantum teleportation, and quantum cryptography. Entanglement detection affects the performance of quantum information processing tasks. Entanglement detection has grown in popularity over the years, and various entanglement detection methods are available, though some have application and system scale limitations. This scoping review sought to identify various measurement methods for entanglement detection in both bipartite and multipartite entanglement systems. Secondary resource indexed literatures were selected based on specific keywords from literatures published between 2017 and 2021. The goal of this study is to present a proposed conceptual framework of entanglement detection based on previous work as a guidance and reference founded on one’s specific requirements.
Quantum technology has been introduced in the IR 4.0, breeding a new era of advanced technology revolutionizing the future. Hence, understanding the key resources of quantum technology, quantum entanglement is vital. Growing interests in quantum technologies has raised comprehensive studies of quantum entanglement, especially on the entanglement classification. Special Linear group, SL(n) of multipartite entanglement classification under the SLOCC protocol is not widely studied due to its complex structure, creating a curb in developing its classification method. Therefore, this paper developed and delivered a classification method of pure multipartite, three-qubit quantum state using a combination of Special Linear group, SL(2) x SL(2) x SL(2) model operator under the SLOCC, classifying entanglement using the model operator with certain selected parameters. Further analysis was done resulting in the determination of the six subgroups, namely fully separable (A-B-C), bi-separable (A-BC, B-AC and C-AB) and genuinely entangled (W and GHZ).
The study introduces the development of the operator model within the Local Unitary (LU) protocol for entanglement classification, specifically of the pure three-qubit quantum systems. Addressing the challenge of accurately distinguishing different classes of entanglement, this research aims to enhance the understanding and utilization of entangled quantum states in quantum information processing. A systematic approach was employed in the development of the model, designed to effectively distinguish different classes of entanglement. This study contributes significantly to quantum information processing, by providing valuable insights into the nature of entangled quantum states and enabling researchers to gain a better understanding, utilizing them effectively in various quantum applications. The developed operator model holds significant potential for the advancements in entanglement classification and broaderscope of quantum information processing. The model marks a notable achievement in enabling a more precise and efficient entanglement of entangled quantum systems, which is crucial for advancing various quantum technologies. Future research should extends this model to a higher-qubit and higher-dimensional quantum systems and explore its integration with several other entanglement classification protocols and Lie groups to further advance the field.