Entanglement-assisted quantum error-correcting codes

量子信息处理(QIP)使用量子现象来执行使用经典资源难以或不可能完成的信息处理任务。这些协议包括使用量子通道的通信协议--例如，通过光纤传输光子--来传输量子或经典信息。一般来说，这些量子通道是有噪声的，导致传输状态的消相干。这种退相干被量子纠错码(QECC)抵消，类似于经典的纠错。这些代码是从经典模型构造的，但有一定的限制：“包含对偶”的限制。PI及其合作者将最常见的“稳定器”代码推广到包括标准QECC和纠缠辅助QECC(EAQECC)。纠缠是比经典关联更强的量子态的一种特性：经典关联不能提高信息传输的速度，但纠缠可以。纠缠是用于隐形传态和密集编码等协议的资源。在纠错中，纠缠既可以提高信息的传输率，也可以增加可纠正的错误数量。EAQECCs可以由任意的经典线性码构造，好的经典码可以产生好的EAQECCs。本课题研究了EAQECCs的性质，它们的构造和应用。PI将研究量子Turbo码、LDPC码和卷积码等码的类别，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--特别是操作码--结合起来，为不同的应用产生具有广泛性质的码族。PI还将研究用于传输经典和量子信息的混合码，以及用于连续变量系统的EAQECC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.