Entanglement-assisted quantum error-correcting codes

点击翻译按钮获取中文摘要

Quantum information processing (QIP) uses quantum phenomena to perform information-processing tasks that are difficult or impossible with classical resources. These include communication protocols using quantum channels--for example, photons through optical fibers--to transmit quantum or classical information. In general, these quantum channels are noisy, causing decoherence of the transmitted states. This decoherence is countered by quantum error-correcting codes (QECCs), analogous to classical error correction. These codes are constructed from classical models, but with a certain restriction: the "dual-containing" constraint. The PI and collaborators have generalized the most common "stabilizer" codes to include both standard QECCs and entanglement-assisted QECCs (EAQECCs).Entanglement is a property of quantum states that are correlated more strongly than classically possible: classical correlations cannot boost the rate of information transmission, but entanglement can. Entanglement is a resource for protocols such as teleportation and dense coding. In error correction, entanglement can either boost the rate of information transmission or increase the number of correctable errors. EAQECCs can be constructed from arbitrary classical linear codes, with good classical codes yielding good EAQECCs.This project explores the properties of EAQECCs, their construction, and applications. The PI will study classes of codes such as quantum Turbo codes, LDPC codes, and convolutional codes, evaluate their performance, and determine the entanglement that they require. He will combine entanglement assistance with other coding ideas-- particularly operator codes--producing families of codes with a broad range of properties for different applications. The PI will also study hybrid codes for transmitting both classical and quantum information, and versions of EAQECCs for continuous-variable systems.