Fig. 1 Proposed end-to-end quantum communication system with adaptive coding for image transmission.

In this study, images with varying spatial information (SI) characteristics are used as an information source. These images are first compressed using either the JPEG or HEIF source encoding methods, converting them into classical bitstreams. For channel coding, polar codes with rates of 2/3, 1/2, 1/3 and 1/4 are considered and these channel coding rates are adaptively changed based on the channel conditions. To maintain a similar bandwidth, source coding rates (quality levels) are adjusted in the source coding process. By varying the quality level in response to different channel coding rates, the overall bitrate remains constant across the channel. Once the classical bitstreams are channel encoded, they are converted into qubit superposition states and these qubit states are then transmitted through the quantum communication channel. At the receiver, quantum measurement operators are applied to convert the received qubit states back into classical bits. After this, the appropriate channel decoding process is performed, corresponding to the applied polar coding rate. Finally, the recovered classical bitstream undergoes source decoding (JPEG or HEIF), reconstructing the final images. The following subtopics explain the details of each part of the proposed framework.

Information Source : In our experiment, a set of eleven images from the Microsoft Common Objects in Context (COCO) dataset [12] is used as the source of data, serving as foundational test images for the study. These images represent a range of spatial features that are considered essential for demonstrating the impact of the proposed framework.

Source Encoder : The selected images are compressed using two different source encoding methods: HEIF and JPEG. JPEG is widely used for lossy compression of digital images, while HEIF offers better compression efficiency and higher image quality. To evaluate the proposed system in a bandwidth-restricted environment, the HEIF and JPEG source coding rates are adjusted according to the channel coding rates, ensuring that the system’s throughput remains nearly constant. After compression, the images are converted to classical bitstreams, sequences of binary data ready for further processing.

Channel Encoder : For channel coding, polar codes are employed with specific rates: 2/3, 1/2, 1/3, and 1/4. Polar codes are a type of error correction code that is known for its capacity-achieving properties and can efficiently handle noise in communication channels. The different rates indicate varying levels of redundancy and error-correcting capabilities, which influence the robustness of the encoded data.

Quantum Encoder : The Hadamard gate is a fundamental quantum operation that creates superposition states, where classical bits are transformed into qubits superposition. This transformation allows the classical information to be transmitted through a quantum communication channel. This process is similar to the method that we proposed in our previous work [11].

Channel : The qubits superposition states are then sent through the quantum communication channel. Unlike classical channels, quantum channels are characterized by the properties of quantum mechanics. But in this process, we use a simple channel model to simulate the quantum channel with varying signal-to-noise ratios (SNR), based on the concept that the behaviour of quantum channels under different SNR conditions can be evaluated using a classical channel with equivalent SNR conditions up to a certain level of noise [13].

Quantum Decoder : At the receiver’s end, quantum measurement operators are applied to the received qubit states as described in [11]. These operators collapse the qubit superposition states back into classical bits. Measurement in quantum mechanics is the process by which quantum information is retrieved from qubits and converted into a format that can be processed by classical systems.

Channel Decoder : The classical bits recovered from quantum measurement are then subjected to channel decoding processes that correspond to the polar coding rates used during encoding. This step involves applying the appropriate decoding algorithm to correct any errors and reconstruct the bitstream accurately.

Source Decoder : Finally, the recovered classical bitstream undergoes source decoding using the same method employed during the source encoding phase (JPEG or HEIF). This step reconstructs the final images from the bitstreams, effectively reversing the compression and encoding processes to retrieve the images as they were before transmission.

To demonstrate the proposed quantum communication system for image transmission, we analyse the average performance of the input images across different SNR conditions and coding rates. By dynamically varying the channel noise, we select the optimal channel coding rate for a given channel SNR of the adaptive coding system.

To ensure a fair comparison with the proposed adaptive coding based quantum communication system, an equivalent classical communication system is employed using the same channel coding rates and binary phase-shift keying (BPSK) modulation. This approach helps maintain consistent bandwidth across both methods. The Peak Signal-to-Noise Ratio (PSNR) and Structural Similarity Index Measure (SSIM) values are computed for images reconstructed using both adaptive coding based quantum and the classical communication systems. These metrics provide quantitative measures of image quality, allowing for a direct comparison of performance between the two systems. By analysing the PSNR and SSIM results, the study assesses the effectiveness of the proposed adaptive coding based quantum communication system relative to the equivalent classical system, identifying advantages in terms of image quality and overall performance.

Results and Discussion: This research focuses on comparing the performance of adaptive coding based quantum communication systems with adaptive coding based classical communication systems. The results reveal significant insights into how each system adapts to varying SNR levels, particularly in terms of image quality and error resilience. Furthermore, both HEIF and JPEG image formats are analysed to understand their performance in these communication systems.

The analysis of PSNR for the HEIF image format, as shown in Figure 2, reveals that adaptive coding offers substantial benefits in preserving signal quality across varying SNR levels. Both quantum (Q) and classical (C) systems exhibit notable improvements when adaptive coding is employed, outperforming their non-adaptive counterparts. Notably, the adaptive coding based quantum system exhibits significantly higher PSNR values compared to the adaptive coding based classical system, particularly in the lower SNR range (below 16 dB). This trend is particularly evident, as the proposed quantum communication system achieves a rapid increase in PSNR starting around 4 dB SNR, indicating its robust performance under noisy conditions.

The results also show that the highest PSNR values achieved with high polar coding rates are lower than those obtained with low polar coding rates due to the bandwidth-restrictive conditions imposed during implementation. However, adaptive coding implementations in both quantum and classical communications can mitigate this issue by switching to higher quality values when the channel SNR improves, as the required optimum polar coding rate decreases.

Therefore, as the SNR increases beyond 16 dB, both systems achieve high PSNR values, reaching up to 65 dB. Notably, the earlier rise in PSNR for the proposed quantum system at low SNR (4-12 dB) demonstrates its capability to maintain high-quality transmission under less-than-ideal conditions.