Quantum random access codes (QRACs) enable multiple classical bits to be encoded into fewer qubits, while allowing only a selected bit to be retrieved with probability greater than the corresponding classical limit. Here, we use $$2 \rightarrow 1$$ and $$3 \rightarrow 1$$ QRACs for simultaneous transmission of multiple binary images through a single quantum data stream. At the receiver, the measurement choice determines which encoded image is reconstructed, while the remaining image information is disturbed by the measurement process. The inherent correct-bit probabilities of these QRACs are approximately 85.4% and 78.9%, respectively. By applying median and morphological filtering to the decoded binary images, we improve the reconstruction accuracy in an image-dependent manner, reaching 99.17% for $$2 \rightarrow 1$$ QRACs and 98.36% for $$3 \rightarrow 1$$ QRACs. We also analyze the effect of depolarizing noise on reconstruction quality using accuracy, peak signal-to-noise ratio, and structural similarity index measure. These results demonstrate a selective-access framework for QRAC-based image transmission with potential applications in controlled image/video transmission.
Quantum random access codes (QRACs) enable multiple classical bits to be encoded into fewer qubits, while allowing only a selected bit to be retrieved with probability greater than the corresponding classical limit. Here, we use 2→1 and 3→1 QRACs for simultaneous transmission of multiple binary images through a single quantum data stream. At the receiver, the measurement choice determines which encoded image is reconstructed, while the remaining image information is disturbed by the measurement process. The inherent correct-bit probabilities of these QRACs are approximately 85.4% and 78.9%, respectively. By applying median and morphological filtering to the decoded binary images, we improve the reconstruction accuracy in an image-dependent manner, reaching 99.17% for 2→1 QRACs and 98.36% for 3→1 QRACs. We also analyze the effect of depolarizing noise on reconstruction quality using accuracy, peak signal-to-noise ratio, and structural similarity index measure. These results demonstrate a selective-access framework for QRAC-based image transmission with potential applications in controlled image/video transmission.
Multi-qubit encoding is a quantum encoding technique that uses multiple qubits to represent information, enabling higher data throughput. This study explores its application in compressed image transmission, comparing its performance to single-qubit encoding in both uncoded and channel-coded configurations. For image compression, JPEG and HEIF formats are used, with source coding rates adjusted to ensure similar bandwidth utilization. The compressed bitstream is optionally protected by channel coding before undergoing quantum encoding using qubit sizes from 1 to 8 for quantum channel transmission. At the receiver, quantum decoding reconstructs classical bits, followed by optional channel decoding, and finally, source decoding restores the image. Image quality is assessed using peak signal-to-noise ratio (PSNR), structural similarity index measure (SSIM) and universal quality index (UQI). Results show that increasing the qubit encoding size improves noise resilience, with eight-qubit encoding achieving a maximum channel SNR gain of 15 dB for JPEG and 17 dB for HEIF under channel coding, demonstrating greater robustness compared to single-qubit encoding but with higher computational complexity. To address this, an adaptive multi-qubit encoding process is proposed, dynamically adjusting qubit usage by utilizing fewer qubits for lower noise levels and higher qubits for higher noise conditions while balancing noise resilience and computational complexity under the assumption of perfect channel estimation.
We consider a communication method, where the sender encodes n classical bits into 1 qubit and sends it to the receiver who performs a certain measurement depending on which of the initial bits must be recovered. This procedure is called (n,1,p) quantum random access code (QRAC) where p > 1/2 is its success probability. It is known that (2,1,0.85) and (3,1,0.79) QRACs (with no classical counterparts) exist and that (4,1,p) QRAC with p > 1/2 is not possible. We extend this model with shared randomness (SR) that is accessible to both parties. Then (n,1,p) QRAC with SR and p > 1/2 exists for any n > 0. We give an upper bound on its success probability (the known (2,1,0.85) and (3,1,0.79) QRACs match this upper bound). We discuss some particular constructions for several small values of n. We also study the classical counterpart of this model where n bits are encoded into 1 bit instead of 1 qubit and SR is used. We give an optimal construction for such codes and find their success probability exactly--it is less than in the quantum case. Interactive 3D quantum random access codes are available on-line at http://home.lanet.lv/~sd20008/racs .
ABSTRACT Achieving reliable high-fidelity image transmission over dynamic channels remains a critical challenge in modern communication systems, particularly in vehicular environments with significant noise impairments. In response, this paper proposes a novel quantum multiple description coding (Q-MDC) framework to enhance image transmission robustness and reconstruction quality. The proposed approach partitions the source image at the pixel level into odd and even components to generate two primary descriptions, which are subsequently converted into bitstreams using various source encoding techniques, including JPEG, JPEG2000, HEIF, and uncompressed formats. These bitstreams are optionally channel encoded and encoded into quantum states in the computational basis. A third correlated description is generated using a controlled-NOT operation, embedding inter-description redundancy while maintaining equal bandwidth across all descriptions. Each description is transformed into quantum superposition states using a Hadamard-based encoder and transmitted over independent noisy channels. At the receiver, inverse Hadamard operations restore the computational basis representation. A packet-wise and qubit-wise deterministic recovery mechanism is then employed to reconstruct corrupted descriptions by exploiting inter-description dependencies. The recovered descriptions are measured, followed by channel decoding and source decoding to reconstruct the image. Simulation results demonstrate that the proposed Q-MDC framework significantly improves peak signal-to-noise ratio (PSNR), structural similarity index (SSIM), and universal quality index (UQI) compared to classical MDC and channel-coded single-stream transmission schemes, achieving SNR gains of up to 4 dB and 7 dB, respectively. The results highlight the effectiveness of the proposed approach for robust multimedia transmission in error-prone wireless environments.INDEX TERMS Image Transmission, Multiple Description Coding (MDC), Noise Resilience, Quantum Communication, Quantum Superposition
While quantum communication can overcome limitations of classical systems, it is limited by fragile quantum states and the complexity of underdeveloped quantum error correction (QEC) methods. This study presents an adaptive multi-qubit QEC scheme for quantum image transmission, where the code rate is dynamically adjusted based on real-time channel conditions to balance error resilience and computational complexity. For this approach, we assume that the receiver has accurate knowledge of the channel conditions to enable effective adaptation. The process begins with source encoding using JPEG and HEIF formats, followed by quantum encoding and multi-qubit QEC using three, five, seven, and nine qubits. The quantum channel encoded data are transmitted through a noisy quantum channel. At the receiver, decoding occurs in three stages: quantum channel decoding, quantum-to-classical conversion (quantum decoding), and source decoding to reconstruct the image. Experimental results show that the proposed system outperforms fixed-rate QEC methods and classical systems, achieving Peak Signal-to-Noise Ratio (PSNR) values of up to 40.51 dB, Structural Similarity Index Measure (SSIM) of up to 0.9730 and Universal Quality Index (UQI) of up to 0.9998 for JPEG images, and PSNR of up to 45.44 dB, SSIM up to 0.9889 and UQI up to 0.9999 for HEIF images.
Achieving reliable high-fidelity image transmission over dynamic channels remains a critical challenge in modern communication systems, particularly in vehicular environments with significant noise impairments. In response, this paper proposes a novel quantum multiple description coding (Q-MDC) framework to enhance image transmission robustness and reconstruction quality. The proposed approach partitions the source image at the pixel level into odd and even components to generate two primary descriptions, which are subsequently converted into bitstreams using various source encoding techniques, including JPEG, JPEG2000, HEIF, and uncompressed formats. These bitstreams are optionally channel encoded and encoded into quantum states in the computational basis. A third correlated description is generated using a controlled-NOT operation, embedding inter-description redundancy while maintaining equal bandwidth across all descriptions. Each description is transformed into quantum superposition states using a Hadamard-based encoder and transmitted over independent noisy channels. At the receiver, inverse Hadamard operations restore the computational basis representation. A packet-wise and qubit-wise deterministic recovery mechanism is then employed to reconstruct corrupted descriptions by exploiting inter-description dependencies. The recovered descriptions are measured, followed by channel decoding and source decoding to reconstruct the image. Simulation results demonstrate that the proposed Q-MDC framework significantly improves peak signal-to-noise ratio (PSNR), structural similarity index (SSIM), and universal quality index (UQI) compared to classical MDC and channel-coded single-stream transmission schemes, achieving SNR gains of up to 4 dB and 7 dB, respectively. The results highlight the effectiveness of the proposed approach for robust multimedia transmission in error-prone wireless environments.
A (Quantum) Random Access Code ((Q)RAC) is a scheme that encodes n bits into m (qu)bits such that any of the n bits can be recovered with a worst case probability p>21. Such a code is denoted by the triple (n,m,p). It is known that n<4m for all QRACs and n<2m for classical RACs. These bounds are also known to be tight, as explicit constructions exist for n=4m−1 and n=2m−1 for quantum and classical codes respectively. We generalize (Q)RACs to a scheme encoding nd-levels into m (qu)-d-levels such that any d-level can be recovered with the probability for every wrong outcome value being less than d1. We construct explicit solutions for all n≤d−1d2m−1. For d=2, the constructions coincide with those previously known. We show that the (Q)RACs are d-parity-oblivious, generalizing ordinary parity-obliviousness. We further investigate optimization of the success probabilities. For d=2, we use the measure operators of the previously best known solutions, but improve the encoding states to give a higher success probability. We conjecture that for maximal (n=4m−1,m,p) QRACs, p=21+(3+1)m−11 is possible and show that it is an upper bound for the measure operators that we use. When we compare (n,m,pq) QRACs with classical (n,2m,pc) RACs, we can always find pq≥pc, but the classical code gives information about every input bit simultaneously, while the QRAC only gives information about a subset. For several different (n,2,p) QRACs, we see the same trade-off, as the best p values are obtained when the number of bits that can be obtained simultaneously is as small as possible. The trade-off is connected to parity-obliviousness, since high certainty information about several bits can be used to calculate probabilities for parities of subsets.