Entanglement, quantum entropy and mutual information
Entanglement, quantum entropy and mutual information
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DOI：
10.1098/rspa.2001.0867
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发表时间：
2002-01-08
影响因子：
3.5
通讯作者：
Ohya, M
中科院分区：
文献类型：
--
作者：
Belavkin, VP;Ohya, M
研究了半有限冯诺依曼代数中量子耦合和量子纠缠的运算结构，并对其进行了分类。我们证明了经典-量子对应，如量子编码，可以被视为对角半经典（d-）耦合，和纠缠，其特征在于真正的量子（q-）耦合，可以被视为真正的量子编码。d-复合态和纠缠态的相对熵导致给定量子态的两种不同类型的熵：冯诺依曼熵，它是在所有d-纠缠上实现的互信息的最大值，以及维度熵，它是在标准纠缠（真正的量子纠缠）下实现的，仅在纯边缘态的情况下与d-纠缠一致。量子噪声信道的d-和q-信息分别通过输入d-和q-编码定义，量子无噪声信道的q-容量被发现是输入代数维数的对数。量子容量可以是经典容量的两倍，作为所有d-耦合（或编码）的上确界，由最大阿贝尔子代数的维数的对数限制。
The operational structure of quantum couplings and entanglements is studied and classified for semi-finite von Neumann algebras. We show that the classical-quantum correspondences, such as quantum encodings, can be treated as diagonal semi-classical (d-) couplings, and the entanglements, characterized by truly quantum (q-) couplings, can be regarded as truly quantum encodings. The relative entropy of the d-compound and entangled states leads to two different types of entropy for a given quantum state: the von Neumann entropy, which is achieved as the maximum of mutual information over all d-entanglements, and the dimensional entropy, which is achieved at the standard entanglement (true quantum entanglement) coinciding with a d-entanglement only in the case of pure marginal states. The d- and q-information of a quantum noisy channel are, respectively, defined via the input d- and q-encodings, and the q-capacity of a quantum noiseless channel is found to be the logarithm of the dimensionality of the input algebra. The quantum capacity may double the classical capacity, achieved as the supremum over all d-couplings (or encodings) bounded by the logarithm of the dimensionality of a maximal Abelian subalgebra.