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Journal of Korean Institute of Industrial Engineers

Quantum Dense Coding Transfer Framework of Phase Damping Channel System using Weak Measurement and Correction Rotation

Jun‐Pyo Hong, Hyunsoo Lee

Published Jun 15, 2024• 1 citation
Publisher

Abstract

Quantum dense coding is one of the important quantum computing techniques in communication. Quantum dense coding uses a small number of qubits for transmitions using the quantum entanglement state, which can deliver more classical bit data. However, during a transmission process, the coherence and quantum entanglement state may collapse owing to the influence of the embedding noise channel that a common quantum computing system has. This issue results in a decrease in the transmission capacity of quantum dense coding. Several techniques have been studied to reduce the influences of quantum noise channels. However, these research studies assumed limited quantum environment. This study proposes a new and effective framework to prevent the collapse of quantum entanglement states, focusing on a time-correlated phase damping channels. The quantum state is analyzed using quantum weak measurement (WM), and a correction rotation (CR) technique is integrated to restore it to its initial phase. The effectiveness of the proposed framework is demonstrated experimentally with the comparisons with existing quantum noise reduction techniques.

DOI
10.7232/jkiie.2024.50.3.202

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Quantum dense coding is one of the important quantum computing techniques in communication. Quantum dense coding uses a small number of qubits for transmitions using the quantum entanglement state, which can deliver more classical bit data. However, during a transmission process, the coherence and quantum entanglement state may collapse owing to the influence of the embedding noise channel that a common quantum computing system has. This issue results in a decrease in the transmission capacity of quantum dense coding. Several techniques have been studied to reduce the influences of quantum noise channels. However, these research studies assumed limited quantum environment. This study proposes a new and effective framework to prevent the collapse of quantum entanglement states, focusing on a time-correlated phase damping channels. The quantum state is analyzed using quantum weak measurement (WM), and a correction rotation (CR) technique is integrated to restore it to its initial phase. The effectiveness of the proposed framework is demonstrated experimentally with the comparisons with existing quantum noise reduction techniques.
Quantum dense coding enables the transmission of two classical bits of information through the exchange of a single qubit, provided that an entangled state is shared between the communicating parties. While this protocol achieves a fundamental increase in channel capacity, its practical realization is strongly influenced by the presence of noise in realistic quantum channels. This work presents a simulation-based study of dense coding performance under two representative noise models: the depolarizing channel and the amplitude damping channel. Using Qiskit Aer, the bit error rate (BER), frame error rate (FER), and effective channel capacity are evaluated across a range of noise parameters. In addition, a classical threefold repetition strategy is examined as a lightweight error-mitigation technique. Results indicate that depolarizing noise produces more rapid degradation in both BER and channel capacity compared to amplitude damping, while repetition coding provides partial improvement in reliability at the expense of resource overhead. These findings highlight the trade-offs between efficiency and robustness in noisy implementations of dense coding and motivate further exploration of more advanced quantum error correction methods.
Based on the quantum technique of the weak measurement and quantum measurement reversal (WMR), we propose a scheme to protect entanglement for an entangled two-qubit pure state from four typical quantum noise channels with memory, i.e., the amplitude damping channel, the phase damping channel, the bit flip channel, and the depolarizing channel. For a given initial state | ψ 〉 = a| 00 〉 + d| 11 〉, it is found that the WMR operation indeed helps to protect entanglement from the above four quantum channels with memory, and the protection effect of WMR scheme is better when the coefficient a is small. For the other initial state | ϕ 〉 = b| 01 〉 + c| 10 〉, the effect of the protection scheme is the same regardless of the coefficient b and the WMR operation can protect entanglement in the amplitude damping channel with memory. Moreover, the protection of entanglement in quantum noise channels without memory in contrast to the results of the channels with memory is more effective. For | ψ 〉 or | ϕ 〉, we also find that the memory parameters play a significant role in the suppression of entanglement sudden death and the initial entanglement can be drastically amplified. Another more important result is that the relationship between the concurrence, the memory parameter, the weak measurement strength, and quantum measurement reversal strength is found through calculation and discussion. It provides a strong basis for the system to maintain maximum entanglement in the nosie channel.
This paper explores a novel approach to error correction codes inspired by the principles of quantum mechanics, specifically quantum entanglement and superposition. Traditional classical error correction codes often struggle to effectively combat noise and interference, particularly in complex systems. This research proposes a new coding scheme that utilizes correlated measurements of entangled qubits to achieve enhanced protection against errors. The core of the method lies in exploiting the inherent correlations present in entangled systems, allowing for a more robust detection and correction of errors compared to conventional techniques. The presented code demonstrates the potential to surpass the limitations of established classical codes by directly leveraging the unique properties of quantum phenomena. We detail the mathematical framework and the theoretical underpinnings of this approach, outlining its potential impact on data transmission and storage in quantum computing and related fields. The key advancements are focused on achieving higher error correction capabilities with a potentially reduced overhead compared to existing solutions. This work lays the foundation for future research and development in quantum-inspired error correction.
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 ∣ψAB⟩=12(∣11⟩+∣00⟩)\left| {{{\mathbf{\psi }}_{{\mathbf{AB}}}}} \right\rangle =\frac{1}{{\sqrt 2 }}\left( {\left| {11} \right\rangle +\left| {00} \right\rangle } \right)∣ψAB​⟩=2​1​(∣11⟩+∣00⟩) 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 coefficientγ\gammaγand coupling strengthη\etaηand 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 capacityχ\chiχof the system, thus ensuring the effective transmission and processing of quantum information in practice. It lays a solid foundation for quantum computing
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.