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International Conference on Communications

Non-binary classical error-correcting codes for quantum communication

Christopher Boyd, Renaud-Alexandre Pitaval, Ülo Parts, Olav Tirkkonen

Published Jun 1, 2015• 4 citations
Publisher

Abstract

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.

DOI
10.1109/icc.2015.7248959

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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.
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.
We have conceived a near-capacity code design for entanglement-assisted classical communication over the quantum depolarizing channel. The proposed system relies on efficient near-capacity classical code designs for approaching the entanglement-assisted classical capacity of a quantum depolarizing channel. It incorporates an Irregular Convolutional Code (IRCC), a Unity Rate Code (URC) and a soft-decision aided Superdense Code (SD), which is hence referred to as an IRCC-URC-SD arrangement. Furthermore, the entanglement-assisted classical capacity of an N-qubit superdense code transmitted over a depolarizing channel is invoked for benchmarking. It is demonstrated that the proposed system operates within 0.4 dB of the achievable noise limit for both 2-qubit as well as 3-qubit SD schemes. More specifically, our design exhibits a deviation of only 0.062 and 0.031 classical bits per channel use from the corresponding 2-qubit and 3-qubit capacity limits, respectively. The proposed system is also benchmarked against the classical convolutional and turbo codes.
We introduce a robust quantum communication protocol that integrates classical error-control coding, entanglement distribution, and superdense coding. Classical error-correcting codes are used to mitigate dark counts and photon losses by determining the positions of qubit transmissions and protecting the data embedded through superdense coding. We derive conditions on the employed codes that guarantee successful error correction under a bounded error-frequency model. Moreover, upper bounds are derived on the performance of conventional superdense coding protected by classical error correction. It is shown that, under the same constraints on error frequency, suitable code configurations of the proposed protocol can exceed those upper bounds both in terms of data rate and energy efficiency. Finally, we develop a physical error model based on fiber attenuation, detector efficiency, dark counts, and time-slot duration, and use it to evaluate the effective performance of different configurations of error-correcting codes. The proposed approach is primarily suited for short-distance quantum links, as in Quantum Local Area Network (QLAN) where it can provide high communication throughput while integrating entanglement distribution directly into the communication process.
Superdense coding proved that entanglement-assisted quantum communications can improve the data transmission rates compared to classical systems. It allows sending 2 classical bits between the parties in exchange of 1 quantum bit and a pre-shared entangled Bell pair. This paper introduces a new protocol which is intended for distributed communication. Using a pre-shared entangled Bell pair and 1 classical bit 2,5 classical bits can be transmitted in average. This means not only valuable increase in capacity but the two-way distributed operation opens new fields of investigation.
This paper proposes a novel communication protocol leveraging multi-particle entanglement for non-classical information transmission. The core of the protocol resides in a carefully designed encoding scheme utilizing multi-variable entangled states to mitigate the impact of quantum decoherence and achieve information transfer rates exceeding the classical channel capacity. We introduce a multi-variable entangled state based error correction coding mechanism, combined with quantum decoherence theory, providing a scalable error correction strategy. The protocol focuses on precise control of entangled state utilization and minimizing errors in non-classical communication, offering a potentially scalable solution. The key mathematical formulation explores the encoding process, error detection, and correction stages, highlighting the role of entangled correlations in recovering the transmitted information. This work contributes to the advancement of quantum communication by providing a robust and scalable approach to non-classical information transfer. ---
Symbol-based iterative decoding is proposed for the transmission of classical Markov source signals over a quantum channel using a three-stage serial concatenation of a convolutional code (CC), a unity-rate code and a two-qubit superdense (SD) protocol. A modified symbol-based maximum a posteriori algorithm is employed for CC decoding to exploit the Markov source statistics during the iterative decoding process. Extrinsic information transfer chart analysis is performed to evaluate the benefit of the extrinsic mutual information gleaned from the CC decoder for sources with different correlations. We evaluate the bit error rate performance of the proposed coding scheme and compare it with the relevant benchmark schemes, including the turbo coding-based SD scheme. We demonstrate that a near-capacity performance can be achieved using the proposed scheme and when utilizing sources having a high correlation coefficient of ρ = 0.9, the proposed coding scheme performs within 0.53 dB from the entanglement-assisted classical capacity.