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Entanglement Dynamics and Quantum Dense Encoding of Heisenberg Spin Chain in Non-Markovian Environment

ShiSheng Tang

Published Feb 28, 2022• 0 citations
Publisher

Abstract

Abstract Quantum entanglement is a special nonlocal association between quantum systems. It is a fundamental feature of the difference between quantum and classical. At the same time, it acts as a very important resource in quantum informatics. Therefore, entanglement plays a noble role in quantum information and quantum computing. Quantum dense coding, as an application of quantum entanglement in practice, is a quantum communication protocol characterized by security and secrecy, which plays a very important role in quantum informatics and cryptography. This paper is mainly in the Non-Markovian environment of Heisenberg Spin chain system, using the quantum dense coding scheme proposed by Bennett et al. to study The dynamics of quantum dense coding channel capacity evolution with time and the entanglement dynamics of the system are discussed in detail.Based on the theoretical knowledge of open quantum systems and the maximum entangled state \(\left| {{{\mathbf{\psi }}_{{\mathbf{AB}}}}} \right\rangle =\frac{1}{{\sqrt 2 }}\left( {\left| {11} \right\rangle +\left| {00} \right\rangle } \right)\) as the initial state, the density matrix of the system evolution over time is obtained by quantum state diffusion method,and the evolution of channel capacity and entanglement over time of Heisenberg spin chains is simulated accurately. The results show that: the capacity and entanglement of dense coded channel oscillate with time and reach different stable values. Environmental correlation coefficient\(\gamma\)and coupling strength\(\eta\)and a play an important role in dense coding and quantum entanglement of quantum systems.Proper selection of parameters can keep the system good entanglement characteristics and increase the channel capacity\(\chi\)of the system, thus ensuring the effective transmission and processing of quantum information in practice. It lays a solid foundation for quantum computing

DOI
10.21203/rs.3.rs-1395185/v1

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Abstract Quantum entanglement is a special nonlocal association between quantum systems. It is a fundamental feature of the difference between quantum and classical. At the same time, it acts as a very important resource in quantum informatics. Therefore, entanglement plays a noble role in quantum information and quantum computing. Quantum dense coding, as an application of quantum entanglement in practice, is a quantum communication protocol characterized by security and secrecy, which plays a very important role in quantum informatics and cryptography. This paper is mainly in the Non-Markovian environment of Heisenberg Spin chain system, using the quantum dense coding scheme proposed by Bennett et al. to study The dynamics of quantum dense coding channel capacity evolution with time and the entanglement dynamics of the system are discussed in detail.Based on the theoretical knowledge of open quantum systems and the maximum entangled state (\left| {{{\mathbf{\psi }}_{{\mathbf{AB}}}}} \right\rangle =\frac{1}{{\sqrt 2 }}\left( {\left| {11} \right\rangle +\left| {00} \right\rangle } \right)) as the initial state, the density matrix of the system evolution over time is obtained by quantum state diffusion method,and the evolution of channel capacity and entanglement over time of Heisenberg spin chains is simulated accurately. The results show that: the capacity and entanglement of dense coded channel oscillate with time and reach different stable values. Environmental correlation coefficient(\gamma)and coupling strength(\eta)and a play an important role in dense coding and quantum entanglement of quantum systems.Proper selection of parameters can keep the system good entanglement characteristics and increase the channel capacity(\chi)of the system, thus ensuring the effective transmission and processing of quantum information in practice. It lays a solid foundation for quantum computing
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.
We study the dynamics of a chain of interacting quantum particles affected by an individual or collective environment(s), focusing on the role played by the environmental quantum correlations over the evolution of the chain. The presence of entanglement in the state of the environment magnifies the non-Markovian nature of the chain’s dynamics, giving rise to structures in figures of merit such as spin entanglement and purity that are not observed under a separable environmental state. Our analysis can be relevant to problems tackling the open-system dynamics of biological complexes of strong current interest.
We study the dynamics of a chain of interacting quantum particles affected by an individual or collective environment(s), focusing on the role played by the environmental quantum correlations over the evolution of the chain. The presence of entanglement in the state of the environment magnifies the non-Markovian nature of the chain's dynamics, giving rise to structures in figures of merit such as spin entanglement and purity that are not observed under a separable environmental state. Our analysis can be relevant to problems tackling the open-system dynamics of biological complexes of strong current interest.
Abstract Quantum discord (QD), super quantum discord (SQD) and optimal dense coding at entangled states of three types of quantum channels, are investigated. The used models include: two-qubit spin squeezing, the two-qubit Heisenberg XYZ model with decoherency and the Jaynes–Cummings model. In the first two models the quantum correlations and the optimal dense coding capacity are calculated in terms of channel parameters, system initial conditions and decoherency rate. It has been found that valid dense coding can exist, although there is no trace of entanglement in the quantum channel. In contrast, despite the presence of entanglement states in the system, there may be no dense coding capacity. We investigate the effects of cavity Fock states on quantum correlations and optimal dense coding in the Jaynes–Cummings model. Cavity Fock states are found to be effective for quantum correlations and optimal dense coding. The common result of all three models is that the dynamic properties of SQD on our channel enable us to determine when and under what conditions the system is suitable for dense coding capacity.
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.
According to the theory that quantum entanglement can be used in quantum dense coding and increase the classical information capacity of a quantum channel, we discuss and compare the upper bound of capacity for dense coding in two case of using entangled input states and using product input states though a noiseless channel, when using a pure entanglement resource and get the result,i. e. , the capacity of dense coding using entangled input states is no larger than the capacity for product input states.