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arXiv quant-ph/0409106quant-ph
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信道群、纠缠态和量子信息的位置

Channel kets, entangled states, and the location of quantum information

Robert B. Griffiths

摘要:

众所周知的纠缠态和噪声量子信道的对偶性是用信道ket来表示的,信道ket是一个合适的三重系统上的纯态,一旦选择了一个框架以允许一组一致的概率,它就可以作为一个预概率来计算例如信道的入口和出口之间的统计相关性。在每一个框架中,普通(经典)信息论的标准概念都适用,并且询问关于一个系统的特定类型的信息是否存在于另一个系统中是有意义的。量子效应出现时,一个单一的预概率是用来计算统计相关性在不同的不兼容的框架,和各种约束的存在和不存在的不同种类的信息表示在一组全有或全无定理,推广或给予一个精确的含义的概念“不可克隆”。"这些定理用于讨论:信息在使用混合态环境建模的量子信道中的位置;由Holevo引入的$CQ$(经典量子)信道;以及信息在量子码的物理载体中的位置。提出了在$p\geq 2$部分系统上,信道和纠缠问题都可以用纯态(作为预概率)来分类,其中混合二分纠缠和简单噪声信道属于$p=3$类,五比特码属于$p=6$类,等等;然后由组成部分的希尔伯特空间的维数,以及其他尚未确定的标准。

英文摘要:

The well-known duality relating entangled states and noisy quantum channels is expressed in terms of a channel ket, a pure state on a suitable tripartite system, which functions as a pre-probability allowing the calculation of statistical correlations between, for example, the entrance and exit of a channel, once a framework has been chosen so as to allow a consistent set of probabilities. In each framework the standard notions of ordinary (classical) information theory apply, and it makes sense to ask whether information of a particular sort about one system is or is not present in another system. Quantum effects arise when a single pre-probability is used to compute statistical correlations in different incompatible frameworks, and various constraints on the presence and absence of different kinds of information are expressed in a set of all-or-nothing theorems which generalize or give a precise meaning to the concept of ``no-cloning.'' These theorems are used to discuss: the location of information in quantum channels modeled using a mixed-state environment; the $CQ$ (classical-quantum) channels introduced by Holevo; and the location of information in the physical carriers of a quantum code. It is proposed that both channel and entanglement problems be classified in terms of pure states (functioning as pre-probabilities) on systems of $p\geq 2$ parts, with mixed bipartite entanglement and simple noisy channels belonging to the category $p=3$, a five-qubit code to the category $p=6$, etc.; then by the dimensions of the Hilbert spaces of the component parts, along with other criteria yet to be determined.

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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