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arXiv 1004.1641quant-ph
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量子信息理论的解耦方法

The decoupling approach to quantum information theory

Frédéric Dupuis

摘要:

量子信息理论研究物理定律对信息处理任务(如数据压缩和噪声信道上的数据传输)的基本限制。这篇论文提出了一般的技术,使人们能够解决许多基本问题的量子信息理论在一个统一的框架。本论文的中心定理证明了一个协议的存在,该协议通过一个任意的噪声量子信道传输部分已知的量子数据。除了这个问题的内在兴趣之外,这个定理还有几个量子信息理论的中心定理作为直接推论。接下来的章节利用这个定理证明了另外两种类型的量子信道,即量子广播信道和在发送端带有边信息的量子信道的新协议的存在性。这些协议还涉及发送量子信息部分已知的接收器与一个单一的使用的信道,并作为推论纠缠辅助和无辅助渐近编码定理。在这两种情况下,纠缠辅助的渐近版本可以被认为是这些问题的经典版本的最佳编码定理的量子版本。最后一章讨论一种称为锁定的纯量子现象。我们证明,它是可能的编码成一个量子态的经典消息,这样,通过删除一个子系统的对数大小相对于其总大小,没有测量可以有显着的相关性的消息。因此,该消息被一个椭圆形大小的密钥“锁定”。本文提出了第一个锁定协议,成功的标准是消息的联合分布和测量结果之间的跟踪距离和它们的边际的乘积足够小。

英文摘要:

Quantum information theory studies the fundamental limits that physical laws impose on information processing tasks such as data compression and data transmission on noisy channels. This thesis presents general techniques that allow one to solve many fundamental problems of quantum information theory in a unified framework. The central theorem of this thesis proves the existence of a protocol that transmits quantum data that is partially known to the receiver through a single use of an arbitrary noisy quantum channel. In addition to the intrinsic interest of this problem, this theorem has as immediate corollaries several central theorems of quantum information theory. The following chapters use this theorem to prove the existence of new protocols for two other types of quantum channels, namely quantum broadcast channels and quantum channels with side information at the transmitter. These protocols also involve sending quantum information partially known by the receiver with a single use of the channel, and have as corollaries entanglement-assisted and unassisted asymptotic coding theorems. The entanglement-assisted asymptotic versions can, in both cases, be considered as quantum versions of the best coding theorems known for the classical versions of these problems. The last chapter deals with a purely quantum phenomenon called locking. We demonstrate that it is possible to encode a classical message into a quantum state such that, by removing a subsystem of logarithmic size with respect to its total size, no measurement can have significant correlations with the message. The message is therefore "locked" by a logarithmic-size key. This thesis presents the first locking protocol for which the success criterion is that the trace distance between the joint distribution of the message and the measurement result and the product of their marginals be sufficiently small.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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