dorsal/arxiv
View SchemaEntanglement, Quantum Entropy and Mutual Information
| Authors | V. P. Belavkin, M. Ohya |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0208111 |
| URL | https://arxiv.org/abs/quant-ph/0208111 |
| DOI | 10.1098/rspa.2001.0867 |
| Journal | Proc. R. Soc. Lond. A 458 (2002) 209--231 |
Abstract
The operational structure of quantum couplings and entanglements is studied and classified for semifinite 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 as 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.
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"abstract": "The operational structure of quantum couplings and entanglements is studied\nand classified for semifinite von Neumann algebras. We show that the\nclassical-quantum correspondences such as quantum encodings can be treated as\ndiagonal semi-classical (d-) couplings, and the entanglements characterized by\ntruly quantum (q-) couplings, can be regarded as truly quantum encodings. The\nrelative entropy of the d-compound and entangled states leads to two different\ntypes of entropy for a given quantum state: the von Neumann entropy, which is\nachieved as the maximum of mutual information over all d-entanglements, and the\ndimensional entropy, which is achieved at the standard entanglement -- true\nquantum entanglement, coinciding with a d-entanglement only in the case of pure\nmarginal states. The d- and q- information of a quantum noisy channel are\nrespectively defined via the input d- and q- encodings, and the q-capacity of a\nquantum noiseless channel is found as the logarithm of the dimensionality of\nthe input algebra. The quantum capacity may double the classical capacity,\nachieved as the supremum over all d-couplings, or encodings, bounded by the\nlogarithm of the dimensionality of a maximal Abelian subalgebra.",
"arxiv_id": "quant-ph/0208111",
"authors": [
"V. P. Belavkin",
"M. Ohya"
],
"categories": [
"quant-ph"
],
"doi": "10.1098/rspa.2001.0867",
"journal_ref": "Proc. R. Soc. Lond. A 458 (2002) 209--231",
"title": "Entanglement, Quantum Entropy and Mutual Information",
"url": "https://arxiv.org/abs/quant-ph/0208111"
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