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arXiv quant-ph/0004069quant-ph
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量子信息理论中的纠缠与复合态

Entanglements and compound states in quantum information theory

Viacheslav P Belavkin, Masanori Ohya

摘要:

从量子复合态的角度对真正描述量子耦合的量子纠缠进行了研究和分类。我们表明,经典量子对应,如量子编码可以被视为d-纠缠导致一类特殊的可分离的复合态。d-复合态和纠缠态的互信息导致给定量子态的两种不同类型的熵:冯诺依曼熵y,它是在所有d-纠缠态上的信息的上确界,以及维熵,它是在标准纠缠态下实现的,真正的量子纠缠,只在交换的情况下与d-纠缠一致。量子无噪声信道的q容量定义为所有纠缠的上确界,并以输入von Neumann代数维数的对数给出。它可以使经典容量加倍,实现为所有半量子耦合(d-纠缠元或编码)的上确界,其由最大阿贝尔子代数的维数的对数限制。

英文摘要:

Quantum entanglements, describing truly quantum couplings, are stu died and classified from the point of view of quantum compound states. We show that c lassical-quantum correspondences such as quantum encodings can be treated as d-entanglements leading to a special class of the separable compound states. The mutual information of the d-compound and entangled states lead to two di fferent types of entropies for a given quantum state: the von Neumann entrop y, which is achieved as the supremum of the information over all d-entanglem ents, and the dimensional entropy, which is achieved at the standard entangl ement, the true quantum entanglement, coinciding with a d-entanglement only in the commutative case. The q-capacity of a quantum noiseless channel, defi ned as the supremum over all entanglements, is given as the logarithm of the dimensionality of the input von Neumann algebra. It can double the classical capacity, achieved as the supremum over all semi-quantum couplings (d-entang lements, or encodings), which is bounded by the logarithm of the dimensional ity of a maximal Abelian subalgebra.

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