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South American Colloquium on Visible Light Communications (SACVLC)

Advantage of Quantum Trellis–Coded Modulation over its Equivalent Classical Channel under Depolarization

Sebastián Seguel, Ismael Soto

Published Oct 22, 2025• 1 citation
Publisher

Abstract

This work demonstrates that a quantum trellis-coded modulation (QTCM) scheme can outperform a probabilistically equivalent classical channel (PCC) under depolarization. Simulations show that QTCM reduces the bit error rate (BER) by $\mathbf{1 5 \%} \boldsymbol{-} \mathbf{4 0 \%}$ compared to PCC and degrades more slowly as the error probability p increases, with statistically significant differences and small-to-moderate effect sizes. We also estimate decoding complexity and throughput, finding that Viterbi decoding for QTCM remains comparable to classical TCM/PCC (about $\mathbf{1. 1 - 1. 2} \times$ runtime overhead at $L \leq 48$ in Python prototypes). The quantum advantage is most visible in intermediate noise regimes, where entanglement and memory preserve correlations useful for decoding, and it is maintained over a broad operating range before converging to the fully mixed limit. These findings support a practical quantum advantage in communications with memory. We outline a path to NISQ validation with error mitigation and approximate decoding, and extensions to channels with realistic memory.

DOI
10.1109/sacvlc67412.2025.11262030

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This work demonstrates that a quantum trellis-coded modulation (QTCM) scheme can outperform a probabilistically equivalent classical channel (PCC) under depolarization. Simulations show that QTCM reduces the bit error rate (BER) by 15%−40%\mathbf{1 5 \%} \boldsymbol{-} \mathbf{4 0 \%}15%−40% compared to PCC and degrades more slowly as the error probability p increases, with statistically significant differences and small-to-moderate effect sizes. We also estimate decoding complexity and throughput, finding that Viterbi decoding for QTCM remains comparable to classical TCM/PCC (about 1.1−1.2×\mathbf{1. 1 - 1. 2} \times1.1−1.2× runtime overhead at L≤48L \leq 48L≤48 in Python prototypes). The quantum advantage is most visible in intermediate noise regimes, where entanglement and memory preserve correlations useful for decoding, and it is maintained over a broad operating range before converging to the fully mixed limit. These findings support a practical quantum advantage in communications with memory. We outline a path to NISQ validation with error mitigation and approximate decoding, and extensions to channels with realistic memory.
Inspired by the success of classical turbo codes, quantum turbo codes (QTCs) have also been conceived for near-hashing-bound transmission of quantum information over memoryless quantum channels. However, in real physical situations, the memoryless channel assumption may not be well justified, since the channel often exhibits memory of previous error events. Here, we investigate the performance of QTCs over depolarizing channels exhibiting memory and we show that they suffer from a performance degradation at low depolarizing probability values. In order to circumvent the performance degradation issue, we conceive a new coding scheme termed quantum turbo coding scheme exploiting error-correlation (QTC-EEC) that is capable of utilizing the error-correlation while performing the iterative decoding at the receiver. The proposed QTC-EEC can achieve convergence threshold at a higher depolarizing probability for channels with a higher value of correlation parameter and achieve performance near to the capacity. Finally, we propose a joint decoding and estimation scheme for our QTC-EEC relying on the correlation estimation (QTC-EEC-E) designed for more realistic quantum systems with unknown correlation parameter. Simulation results reveal that the proposed QTC-EEC-E can achieve the same performance as that of the ideal system of known correlation parameter and hence demonstrate the accurate estimation of the proposed QTC-EEC-E.
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.
The past, the current state-of-the-art and the future of wireless communications was briefly summarized in [1], [2]. Against this background, this presentation briefly reports on some of the recent quantum-aided design examples in the field of wireless communications. The high complexity of numerous optimal classic communication schemes, such as that of the Maximum Likelihood (ML) Multi-User Detector (MUD) often prevents their practical implementation [3], [4]. Fortunately the parallel-processing capability of quantum-domain algorithms is capable of potentially circumventing this limitation. In our first design example [5] we follow a quantum-aided approach to achieve the same performance as the optimal soft-input soft-output classic detectors by replacing them with a quantum algorithm which estimates the weighted sum of a function's evaluations. We propose a soft-input soft-output Quantum-assisted MUD (QMUD) scheme, which is the quantum-domain equivalent of the Maximum Likelihood (ML) MUD. We then demonstrate its application using the design example of a Direct-Sequence Code Division Multiple Access (DS-CDMA) system employing Bit-Interleaved Coded Modulation (BICM) relying on Iterative Decoding (ID), and compare it to the optimal ML MUD in terms of its performance and complexity. Both our EXtrinsic Information Transfer (EXIT) charts and Bit Error Ratio (BER) curves show that the performance of the proposed QMUD and that of the optimal classic MUD are equivalent, but the QMUD’s computational complexity is significantly lower. In our second design example [6] 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 [7] 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.
In this paper, we propose a new type of code called Trellis-based Quasi-Cyclic (TQC)-LDPC convolutional code, which is a special case of protograph-based LDPC convolutional codes. The proposed TQC-LDPC convolutional code can be derived from any QC-LDPC block code by introducing trellis-based convolutional dependency to the code. The main advantage of the proposed TQC-LDPC convolutional code is that it allows reduced decoder complexity and input granularity (which is defined as the minimum number of input information bits the code requires to generate a codeword) while maintaining the same bit error-rate as the underlying QC-LDPC block code ensemble. We also propose two related power-efficient encoding methods to increase the code rate of the derived TQC-LDPC convolutional code. The newly derived short constraint length TQC-LDPC convolutional codes enable low complexity trellis-based decoders and one such decoder is proposed and described in this paper (namely, QC-Viterbi). The TQC-LDPC convolutional codes and the QC-Viterbi decoder are compared to conventional LDPC codes and Belief Propagation (BP) iterative decoders with respect to bit-error-rate (BER), signal-to-noise ratio (SNR), and decoder complexity. We show both numerically and through hardware implementation results that the proposed QC-Viterbi decoder outperforms the BP iterative decoders by at least 1 dB for same complexity and BER. Alternatively, the proposed QC-Viterbi decoder has 3 times lower complexity than the BP iterative decoder for the same SNR and BER. This low decoding complexity, low BER, and fine granularity makes it feasible for the proposed TQC-LDPC convolutional codes and associated trellis-based decoders to be efficiently implemented in high data rate, next generation mobile systems.
Can entangling codewords across independent uses of a quantum channel improve the rate of classical communication? An old conjecture states that there is no such entanglement advantage for all channels. Although Hastings's result and follow-up works disproved this conjecture, it turns out that enormous dimension is required to construct a channel where entanglement enhances classical communication. This indicates that there might be no entanglement advantage for many physical channels, or for all low dimensional channels. Motivated by recent progress on (generalized) amplitude damping channels, we propose a general Schur-weighted block entropy inequality, and show that there is no entanglement advantage for all phase-covariant channels including multi-level amplitude damping channels, generalized dephasing channels, and damping-dephasing channels. As a by-product, we also recover the recently established result that there is no entanglement advantage for all qubit channels.