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IEEE International Conference on Electronics, Computing and Communication Technologies (CONECCT)

Superdense Coding Through Repeaterless Hybrid Network of Depolarizing Quantum Communication Channels

Gokul Srinivasan, Shantom Kumar Borah, Sainath Bitragunta

Published Jul 9, 2021• 4 citations
Publisher

Abstract

Superdense coding is a fundamental protocol in quantum communication, which enables us to send two bits of information by the transmission of just a single qubit. In this paper, we consider superdense coding through a noisy quantum depolarizing channel. Following a simple calculation, we derive superdense coding capacity as a function of depolarizing probability. We extend this derivation to the scenario of repeaterless series-cascaded depolarizing channels and provide an elementary approach to evaluate the maximal intervals in which repeaters shall need to be placed in such a cascaded system. Finally, we validate the theoretical results via a Monte Carlo simulation, simultaneously providing a generalized framework. We believe that our numerical results serve as a useful benchmark and give a base to extend such simulations to other quantum channels.

DOI
10.1109/conecct52877.2021.9622362

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Superdense coding is a fundamental protocol in quantum communication, which enables us to send two bits of information by the transmission of just a single qubit. In this paper, we consider superdense coding through a noisy quantum depolarizing channel. Following a simple calculation, we derive superdense coding capacity as a function of depolarizing probability. We extend this derivation to the scenario of repeaterless series-cascaded depolarizing channels and provide an elementary approach to evaluate the maximal intervals in which repeaters shall need to be placed in such a cascaded system. Finally, we validate the theoretical results via a Monte Carlo simulation, simultaneously providing a generalized framework. We believe that our numerical results serve as a useful benchmark and give a base to extend such simulations to other quantum channels.
This thesis investigates the feasibility of utilising classical error-correcting codes in quantum communications, specifically in the entanglement-assisted communication of classical information over quantum depolarising channels. A classical-quantum communication system is presented, which relies on error-correction in the classical domain to achieve a classical information rate that approaches the entanglement-assisted capacity of a depolarising channel. Classical information is transmitted over the quantum channel by means of the superdense coding protocol. Different scenarios for the system are considered, including the noiseless and noisy distribution of initial entanglement resources and the use of higher-order entangled states. The overall transmission model corresponding to each scenario is shown to reduce to a classical, discrete and memoryless channel. The capacities of these equivalent classical channels are derived, and an inherent capacity loss when binary classical error correcting codes are employed is identified, motivating the use of non-binary codes. It is ultimately demonstrated that duo-binary turbo codes outperform binary turbo codes in all investigated scenarios, a result of the former's ability to exploit correlations between the pairs of classical bits communicated via the superdense coding protocol.
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.
We investigate the use of non-binary classical error-correcting codes in facilitating reliable, entanglement-assisted communication of classical information over quantum depolarising channels. A classical-quantum communication system is presented, which relies on error-correction in the classical domain to achieve an information rate that approaches the entanglement-assisted capacity of the quantum channel. Classical information is transmitted over the channel by means of the superdense coding protocol, and the impact of the noisy distribution of initial entanglement resources on the achievable information rate is considered. In this context, the transmission model is equivalent to a non-binary discrete symmetric classical channel, which motivates the use of non-binary error-correcting codes capable of exploiting correlations between the pairs of classical bits communicated via the superdense coding protocol. We illustrate this principle by showing that duo-binary turbo codes significantly outperform binary turbo codes in the considered scenarios.
Quantum communication is at the heart of the quantum information theory. We study two types of quantum communication protocols over noisy transmission channels, i.e. super dense coding and cryptography protocols. In the first part of this thesis, for various scenarios, it is discussed how the super dense coding capacity is influenced by noisy quantum channels. The case of memoryless channels as well as those channels with memory which are modelled by uncorrelated and correlated noise, respectively, are considered. Explicitly Pauli channels over arbitrary dimensions are treated and the super dense coding capacity for some resource states is derived. For the qubit depolarizing channel, when noise is uncorrelated, the super dense coding capacity with respect to the input state is also optimized. This illustrates a threshold value of the noise parameter below which the super dense coding capacity is optimized by a maximally entangled initial state, while above the threshold value the super dense coding capacity is optimized by a product state. For Pauli channels, with correlated noise, the case of non unitary encoding is studied and the super dense coding capacity is derived. The first part of this thesis is concluded with an example for multipartite super dense coding. In the second part of the thesis, the problem of optimal eavesdropping on noisy states in quantum key distribution is investigated. The case of the six state protocol, when the signal states are mixed with white noise, is considered. This situation may arise either when Alice deliberately adds noise to the signal states before they leave her lab, or, in a realistic scenario when the eavesdropper (referred to as Eve) is not assumed to replace the noisy quantum channel by a noiseless one. For individual attacks, we find Eve's optimal mutual information with Alice as a function of the quantum bit error rate. Finally, the results illustrate that adding noise on the quantum level can make quantum key distribution more robust against eavesdropping.
Using the theory of quantum trajectories, we study the classical capacity C\mathbf{C}C of noisy quantum channels in the superdense coding protocol. We apply the two models that generalize single-qubit noisy channels, such as amplitude damping and phase flip, to the many-qubit situation. Our numerical results show that the quantum trajectory approach is suitable for modeling the superdense coding protocol in realistic environments.