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Interdisciplinary Humanities and Communication Studies

Multipartite Dense Coding in Social Internet of Things

Yao Zhang

Published Jun 1, 2023• 0 citations
Publisher

Abstract

The world today is interconnected. As we live in the contemporary era, we will undoubtedly feel the importance of information interaction in all aspects. This kind of information interaction needs to be carried out or mediated. Quantum communication is a new way of information interaction that has been pushed to the forefront in the past decade. It not only has the low cost of traditional radio communication but also has the characteristics of long relay distance of optical communication system. Compared with these characteristics, the most important thing is that it has super high confidentiality. This is the most critical point in the information age. Dense coding is an important application of quantum information. It reflects the difference between quantum bits and classical bits in transmission, providing a reliable theoretical basis for improving the effectiveness of remote communication in the future. We discuss two kinds of extensions of the original dense coding. They respectively work for high-dimension and multipartite situations. We give the laws of the two attachments. In the high-dimensional system, we use the Bell state as the target state of any quantum state and realize the one-to-one correspondence between the entangled state and the Bell state. In multipartite space, we can find that the transformation results can form a dimensional space, and the quantum states obtained are one-to-one, corresponding to the classical bit states. In the multipartite system, we can get the transmitted information more efficiently and accurately by limiting data processing by partial senders. At the same time, this restriction will not reduce the amount of information transmitted initially. Therefore, this limited transformation can improve quantum computing power without damaging quantum states.

DOI
10.61173/p9cdef34

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The world today is interconnected. As we live in the contemporary era, we will undoubtedly feel the importance of information interaction in all aspects. This kind of information interaction needs to be carried out or mediated. Quantum communication is a new way of information interaction that has been pushed to the forefront in the past decade. It not only has the low cost of traditional radio communication but also has the characteristics of long relay distance of optical communication system. Compared with these characteristics, the most important thing is that it has super high confidentiality. This is the most critical point in the information age. Dense coding is an important application of quantum information. It reflects the difference between quantum bits and classical bits in transmission, providing a reliable theoretical basis for improving the effectiveness of remote communication in the future. We discuss two kinds of extensions of the original dense coding. They respectively work for high-dimension and multipartite situations. We give the laws of the two attachments. In the high-dimensional system, we use the Bell state as the target state of any quantum state and realize the one-to-one correspondence between the entangled state and the Bell state. In multipartite space, we can find that the transformation results can form a dimensional space, and the quantum states obtained are one-to-one, corresponding to the classical bit states. In the multipartite system, we can get the transmitted information more efficiently and accurately by limiting data processing by partial senders. At the same time, this restriction will not reduce the amount of information transmitted initially. Therefore, this limited transformation can improve quantum computing power without damaging quantum states.
Abstract Quantum communication is a new emerging inter-discipline in which classical communication theory and quantum mechanics are intertwined. Among them, the utilization of quantum entangled state properties is fundamental to the realization of quantum communication. In this way, we can ensure the security and confidentiality of information during transmission based on a new communication scheme, i.e., a quantum dense coding scheme. It enables the transmission of two bits of classical information by transmitting only one qubit. In the past decades, the scheme has attracted the attention of many researchers because of its promising development. In this paper, on top of quantum mechanics, we first review the two-dimensional dense coding scheme and analyze the process implemented by the above scheme. Then it is successfully extended to higher dimensions (three dimensions), predicting the possibility of implementation in more than two dimensions. Finally, the importance of the maximally entangled state for the transmission of this scheme is briefly explained.
Dense coding is a new concept of quantum communication using the nonlocal feature of quantum entangled states. Bob, the information receiver, prepares polarization-entangled photon twins and sends one of them to Alice, the information sender, while retaining the other. She can prepare each of the four Bell states by operating an appropriate manipulation only on the transmitted photon and thus she can encode 2 bits of information. To decode the 2 bits, Bob must execute a joint measurement of the returned and retained photons with a Bell-state analyzer, such as a Hong-Ou-Mandel type of two-photon interferometer. The information capacity of the transmitted photon is limited by the number of usable nonlocal quantum states which can be prepared through the local operation on one photon. A question arises as to whether Alice can enhance the capacity or not, by adopting an additional degree of freedom by use of pulse position modulation or optical frequency modulation for the transmitted photon. At a glance, capacity enhancement appears to be possible by introducing another degree of freedom. The question here is, however, whether or not it is possible by manipulating only one of photon twins. In the paper, however, we show that the information capacity in dense coding can be enhanced from the reported 2 bits to 3 bits provided that photon twins have spectral correlation and a perfect Bell state analyzer is available.
The aim of the research is the mathematical analysis of quantum superdense coding based on quantum entanglement to increase the efficiency and reliability of information transmission in quantum communication systems. The essence of quantum superdense coding is the ability to transmit two classical bits of information using one qubit, which is part of an entangled pair. The fundamental principles of the superdense quantum coding method are considered. The relevance of the research in the context of the development of secure quantum communications and optimization of information transmission in quantum networks is substantiated. A review of modern scientific publications devoted to the theoretical principles of superdense coding is conducted, which indicate the development potential and practical prospects of this direction of quantum informatics. The analysis of mathematical modeling of quantum superdense encoding and decoding is performed using two alternative approaches – projective measurement in the Bell basis and the inverse Bell transform. It is shown that both approaches allow for the complete recovery of classical information transmitted using entangled quantum states. The advantage of the inverse Bell transform is the simplicity of implementation on quantum devices, the flexibility and accuracy of information processing, and the possibility of scaling, which makes it a reasonable choice in many practical applications. The influence of noise and decoherence on the efficiency of superdense coding has been studied, which is a critical factor in the practical implementation of this method in real quantum systems. A mathematical model of data transmission through a quantum channel under the action of additive white noise has been constructed. An analytical dependence of the probability of correct information recovery on the noise level has been established, which allows us to estimate the limits of reliability of superdense coding in noisy environments. Based on the research, the prospects for the practical application of superdense coding in quantum communication networks, in particular the quantum Internet, as well as in quantum computing and information security systems, have been outlined. The results obtained contribute to the further development of quantum technologies and can be used to create new protocols for highly efficient quantum data transmission.
Quantum communication, as a vital area of quantum information science, aims to leverage quantum phenomena—particularly entanglement—to achieve tasks that are impossible or inefficient in classical systems. It plays a key role in the development of secure communication protocols and advanced information processing. This paper focuses on one such protocol, dense coding, which enables the transmission of two classical bits using only one entangled quantum particle.”We introduce the mathematical and physical foundations of quantum communication, such as the entangled state and Kronecker product. Then we propose the quantum communication protocol, namely dense coding using Bell states. It offer unique advantages that are beyond the classical parts. For this purpose, we in detail analyze the quantum measurements using Pauli gates and identity matrix, as well as the transmission of particle from Alice to Bob. They are necessary steps for dense coding. Then we analyze how Bob finishes the protocol using measurement over two qubits.
A highly entangled bipartite quantum state is more advantageous for the quantum dense coding protocol than states with low entanglement. Applications of quantum channels are most likely to be commercially important only in the multiparty regime, where such a correspondence does not exist even for pure quantum states. We establish a connection between the multiparty capacity of classical information transmission in quantum dense coding and several multipartite quantum correlation measures of the shared state, used in the dense coding protocol. In particular, we show that for the noiseless channel, if multipartite quantum correlations of an arbitrary multipartite state of arbitrary number of qubits are the same as those of the corresponding generalized Greenberger-Horne-Zeilinger state, then the multipartite dense coding capability of the former is the same as or better than that of the generalized Greenberger-Horne-Zeilinger state. Interestingly, in a noisy-channel scenario, where we consider both uncorrelated and correlated noise models, the relative abilities of the quantum channels to transfer classical information can get inverted by administration of a sufficient amount of noise. When the shared state is an arbitrary multipartite mixed state, we also establish a link between the classical capacity for the noiseless case and multipartite quantum correlation measures.