Entanglement-assisted quantum error-correcting codes

量子信息处理（QIP）利用量子现象来完成经典资源难以或不可能完成的信息处理任务。其中包括使用量子通道的通信协议——例如，通过光纤的光子——来传输量子或经典信息。一般来说，这些量子信道是有噪声的，导致传输态的退相干。这种退相干被量子纠错码（QECCs）抵消，类似于经典的纠错。这些代码是根据经典模型构建的，但有一定的限制：“双重包含”约束。PI和合作者已经概括了最常见的“稳定剂”代码，包括标准QECCs和纠缠辅助QECCs （EAQECCs）。纠缠是量子态的一种特性，它的相关性比经典的可能性更强：经典的相关性不能提高信息传输的速率，但纠缠可以。纠缠是传送和密集编码等协议的资源。纠错中，纠缠可以提高信息的传输速率，也可以增加可纠错的数量。EAQECCs可以由任意经典线性码构造，好的经典码产生好的EAQECCs。本项目探讨了EAQECCs的特性、结构和应用。PI将研究诸如量子Turbo码、LDPC码和卷积码之类的代码，评估它们的性能，并确定它们所需的纠缠。他将把纠缠辅助与其他编码思想结合起来——特别是操作员代码——为不同的应用程序生产具有广泛属性的代码族。PI还将研究用于传输经典和量子信息的混合代码，以及用于连续变量系统的EAQECCs版本。

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.