Quantum Error Correction Inapplicable to Really Entangled States

Masataka Ohta

QEC (Quantum Error Correction) assumes that qubit states are disturbed by errors primarily through interactions with their local environment states. The problem is that, when quantum states are superpositioned, QEC improperly assumes all the superpositioned terms share same local environment states and resulting errors though they are, in general, different term by term to which QEC with the fixed number of syndrome qubits is, except for some slightly superpositioned states such as two terms ones, not applicable. Further, fundamental difficulty to scale quantum parallelism regardless of implementation and physical details is derived from theory of Shannon.

Ivan B. Djordjević

Tohya Hiroshima, Masahito Hayashi

Ying Dong, Xiu–Hao Deng, Mingming Jiang +2 more

Via explicit examples we show that the pre-existing entanglement can really enhance (not only behave as an assistance for) the efficiency of the quantum error-correcting codes (QECCs) in a single block of encoding or decoding as well as help in beating the quantum Hamming bound. A systematic approach to constructing entanglement-assisted (or enhanced) quantum error-correcting codes (EAQECCs) via graph states is also presented, and an infinite family of entanglement-enhanced codes has been constructed. Furthermore we generalize the EAQECCs to the case of not-so-perfectly protected qubit and introduce the quantity infidelity as a figure of merit and show that the EAQECCs also outperform the ordinary QECCs.

Jincheng Zhang

Quantum information is increasingly vital for modern technologies, including secure communication and advanced computation. However, the fragile nature of quantum states makes them susceptible to errors during transmission and storage. This paper proposes a novel quantum error correction (QEC) scheme based on the principle of quantum entanglement, aiming to significantly enhance the security of quantum communication. We detail the design of a QEC protocol utilizing entangled qubit states to detect and correct errors, offering a promising pathway toward building robust quantum networks. The core claim is that this method can achieve high error correction rates and secure quantum communication using the unique properties of entanglement.