Encoding schemes and error-correcting codes are widely used in information technology to improve the reliability of data transmission over real-world communication channels. Quantum information protocols can further enhance the performance in data transmission by encoding a message in quantum states; however, most proposals to date have focused on the regime of a large number of uses of the noisy channel, which is unfeasible with current quantum technology. We experimentally demonstrate quantum enhanced communication over an amplitude damping noisy channel with only two uses of the channel per bit and a single entangling gate at the decoder. By simulating the channel using a photonic interferometric setup, we experimentally increase the reliability of transmitting a data bit by greater than
20 for a certain damping range over classically sending the message twice. We show how our methodology can be extended to larger systems by simulating the transmission of a single bit with up to eight uses of the channel and a two-bit message with three uses of the channel, predicting a quantum enhancement in all cases.
Abstract The classical noisy-channel coding theorem developed by Shannon establishes a fundamental limit on reliable information transmission. In quantum regime, this framework is extended by results such as the Lloyd-Shor-Devetak theorem, which gives the hashing limit on quantum channel capacity. In this work, we beat the hashing limit for low rate coding schemes over quantum Pauli channels. Our approach is based on a re-examination of Bacon-Shor codes and their generalizations, which we show are not merely simple constructions but instances of a broader mechanism that fundamentally alters achievable rate limits. Over depolarizing channels with depolarizing probability of p, these codes exceed the hashing bound with 0.1145 ≤ p ≤ 0.75, and further surpass the asymptotic quantum Singleton bound under bounded minimum-distance decoding for 0.3301 ≤ p ≤ 0.75. We further present explicit constructions based on quantum low-density parity-check codes, achieving frame error rates below 10−4 while exceeding the hashing bound. The advantage persists and is pronouncedly enhanced in the presence of biased noise, demonstrating robustness across realistic quantum Pauli channels. Our results challenge the prevailing understanding of fundamental limits in quantum coding and information theory.
This paper explores a novel approach to quantum information encoding and decoding by leveraging the dynamic topology of quantum entanglement. Traditional quantum information processing methods largely rely on static entangled states, potentially limiting information transmission rates. We propose a system architecture incorporating multiple controlled quantum bits (qubits) exhibiting dynamic entanglement. Through precise manipulation of qubit positions and interactions, we harness the topological changes within the entanglement to encode and decode information. A topological optimization algorithm is then introduced, continuously adjusting the system's qubit topology based on information transmission efficiency and entanglement stability criteria. The core claim is that this dynamic topological control enables optimization of the encoding and decoding process, potentially surpassing the classical information transmission limit. The fundamental mechanisms involve exploiting the temporal evolution of entanglement, coupled with a feedback control loop driven by topological optimization. Mathematical formulations are presented to describe the key components of the system, including the entanglement entropy, the topological optimization objective function, and the dynamics of the qubit positions. This work represents a significant step toward realizing more efficient and robust quantum information networks. ---