Quantum Random Access Codes Achieve Conjectured Bound of Average Success Probability

Researchers have long sought to optimise Random Access Codes (QRACs) , essential tools balancing data compression and accessibility , for quantum computation. Takayuki Suzuki of SCSK Corporation, alongside colleagues, present a novel analytical construction method for QRACs, tackling a previously unsolved problem of deriving optimal codes for general dimensions. Their work demonstrably achieves the long-conjectured upper bound on average success probability for all dimensions, offering a significant step towards scalable, high-dimensional information processing. Crucially, the team’s design allows for implementation with minimal circuit depth, even with limited qubit connectivity, and provides fresh understanding of the fundamental limits between classical and quantum information theory.

Optimal (n, n-1) QRACs Analytically Constructed yield efficient

Scientists have achieved a breakthrough in quantum random access codes (QRACs), establishing an analytical construction method for codes encoding n bits of classical information into n-1 qubits. This research directly addresses a long-standing open problem in quantum information theory, the analytical derivation of optimal codes for general n. The team rigorously proves that their construction achieves the numerically conjectured upper bound of average success probability, specifically P = 1/2 + p(n-1)/n/2, for all values of n. This accomplishment not only validates existing numerical predictions but also provides a foundational theoretical model for verifying quantum advantage in high-dimensional spaces.

The study employs an explicit operator formalism to build these (n, n-1)-QRACs, offering a systematic approach to code construction. Crucially, the researchers present a novel algorithm to decompose the derived optimal Positive Operator-Valued Measure (POVM) into standard quantum gates, facilitating practical implementation. This decomposition results in a decoding circuit comprised solely of interactions between adjacent qubits, enabling implementation with a Circuit depth of O(n) even under the constraints of linear qubit connectivity, a significant advantage for current quantum hardware architectures. This scalable implementation method promises to advance high-dimensional quantum information processing considerably.

Furthermore, the work delves into the high-dimensional limit, revealing that while the non-commutativity of measurements diminishes as dimensionality increases, an unavoidable information-theoretic gap of O(log n) from the Holevo bound emerges due to symmetric encoding with pure states. This finding provides new insights into the fundamental mathematical structure at the quantum-classical boundary, highlighting the inherent trade-offs between compressibility and accessibility of information in quantum systems. The research establishes a valuable theoretical model for understanding how quantum advantage is demonstrated for all finite n and how the bound is formed. This analytical construction is more than a theoretical proof; it offers concrete practical utility.

The proposed decoding circuit, with its limited qubit interactions, is ideally suited for implementation on existing quantum computing platforms like superconducting qubits, which often face limitations in all-to-all connectivity. By circumventing the need for complex SWAP gates, the O(n) circuit depth represents a substantial improvement in efficiency and scalability. This work addresses a long-standing problem in quantum information theory, the analytical derivation of optimal codes for encoding classical information into qubits, specifically focusing on the trade-off between compressibility and accessibility. Researchers proved this construction strictly achieves the numerically conjectured upper bound of average success probability, P = 1/2 + p(n −1)/n/2, for all values of n, a significant advancement in the field. The study pioneers a systematic algorithm to decompose the derived optimal Positive Operator-Valued Measure (POVM) into standard quantum gates, simplifying implementation.

Experiments employed an operator formalism to build the (n, n −1)-QRACs, encoding n bits of classical information into n −1 qubits, thereby providing an ideal model for verifying quantum advantage in high-dimensional spaces. The resulting decoding circuit, crucially, consists solely of interactions between adjacent qubits, enabling implementation with a circuit depth of O(n) even under linear connectivity constraints. This innovative circuit design represents a substantial improvement in scalability for high-dimensional quantum information processing. Furthermore, the team analysed the high-dimensional limit, revealing that while the non-commutativity of measurements is suppressed, an unavoidable information-theoretic gap of O(log n) from the Holevo bound arises during symmetric encoding.

The approach enables a scalable implementation method for high-dimensional quantum information processing, offering new insights into the quantum-classical boundary. Scientists harnessed this methodology to rigorously demonstrate the validity of the numerically conjectured bound for all n, a result previously unproven analytically. This study not only confirms existing numerical predictions but also provides a concrete code construction that achieves optimal performance, advancing the understanding of fundamental limits in quantum information theory. The research, published recently, establishes a method for constructing (n, n-1)-QRACs, demonstrating that these codes strictly achieve a numerically conjectured upper bound of average success probability for all values of n. This breakthrough delivers a scalable implementation method for high-dimensional information processing and offers new insights into the mathematical structure at the quantum-classical boundary. Experiments revealed that the team rigorously proved the achievability of the conjectured bound, establishing the class of (n, n-1)-QRACs as a valuable theoretical model for understanding quantum advantage for finite n.

The work details an explicit operator formalism used to construct these codes, allowing for precise control over the encoding and decoding processes. Measurements confirm that the derived optimal Positive Operator-Valued Measure (POVM) can be systematically decomposed into standard quantum gates, simplifying practical implementation. Tests prove that the resulting decoding circuit requires a circuit depth of O(n) even under linear connectivity constraints, a significant advantage for current quantum hardware. Data. Results demonstrate that the optimal POVM for decoding was constructed using projection operators onto subspaces corresponding to specific bit values, maximizing the average success probability.

The team analytically derived the optimal measurement strategy, achieving a success probability of Pconj n,n−1 for the (n, n-1) case. Furthermore, analysis of the high-dimensional limit (n →∞) revealed that while state disturbance due to non-commutativity is suppressed by O(1/n), an unavoidable information-theoretic gap of O(log n) arises from the Holevo bound, representing a fundamental cost of symmetric encoding with pure states. This study not only provides a scalable implementation but also deepens our understanding of the limits of quantum information processing.

Optimal (n, n-1)-QRACs Constructed and Decomposed yield efficient

Scientists have established an analytical construction method for optimal quantum random access codes (QRACs), specifically addressing the (n, n-1)-QRACs, which encode n-1 classical bits into n qubits. This achievement resolves a long-standing problem previously addressed only through numerical conjecture. The research demonstrates that the constructed codes achieve the theoretically predicted upper bound on average success probability for all values of n, offering a significant step forward in quantum information processing. Furthermore, researchers developed a systematic algorithm to decompose the optimal measurement into standard quantum gates.

This decomposition results in a decoding circuit with a depth of O(n) even with limited qubit connectivity, making the protocol operationally accessible and scalable. Analysis of the high-dimensional limit revealed an unavoidable information-theoretic gap from the Holevo bound for symmetric encoding, while also showing that non-commutativity of measurements is suppressed. The authors acknowledge that the quantum advantage demonstrated by this protocol diminishes with increasing dimension, scaling as O(1/n)0.6, and requires a substantial number of measurements, scaling as O(n2), to achieve statistical significance. This poses experimental challenges due to the potential for physical noise to obscure the advantage. However, they emphasize the value of the (n, n-1)-QRACs as a rigorous benchmark for assessing the effective dimension of quantum devices, functioning as a quality assurance metric. Future research could focus on mitigating the effects of noise and improving the efficiency of implementations to make this benchmark more feasible, potentially exploring error correction techniques or tailored hardware designs.