dorsal/arxiv
View SchemaOn Entangled Information and Quantum Capacity
| Authors | V. P. Belavkin |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0208115 |
| URL | https://arxiv.org/abs/quant-ph/0208115 |
| Journal | Open Sys. & Information Dyn. 8: 1-18, 2001 |
Abstract
The pure quantum entanglement is generalized to the case of mixed compound states on an operator algebra to include the classical and quantum encodings as particular cases. The true quantum entanglements are characterized by quantum couplings which are described as transpose-CP, but not Completely Positive (CP), trace-normalized linear positive maps of the algebra. The entangled (total) information is defined in this paper as a relative entropy of the conditional (the derivative of the compound state with respect to the input) and the unconditional output states. Thus defined the total information of the entangled states leads to two different types of the entropy for a given quantum state: the von Neumann entropy, or c-entropy, which is achieved as the supremum of the information over all c-entanglements and thus is semi-classical, and the true quantum entropy, or q-entropy, which is achieved at the standard entanglement. The q-capacity, defined as the supremum over all entanglements, coincides with the topological entropy. In the case of the simple algebra it doubles the c-capacity, coinciding with the rank-entropy. The conditional q-entropy based on the q-entropy, is positive, unlike the von Neumann conditional entropy, and the q-information of a quantum channel is proved to be additive.
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"abstract": "The pure quantum entanglement is generalized to the case of mixed compound\nstates on an operator algebra to include the classical and quantum encodings as\nparticular cases. The true quantum entanglements are characterized by quantum\ncouplings which are described as transpose-CP, but not Completely Positive\n(CP), trace-normalized linear positive maps of the algebra.\n The entangled (total) information is defined in this paper as a relative\nentropy of the conditional (the derivative of the compound state with respect\nto the input) and the unconditional output states. Thus defined the total\ninformation of the entangled states leads to two different types of the entropy\nfor a given quantum state: the von Neumann entropy, or c-entropy, which is\nachieved as the supremum of the information over all c-entanglements and thus\nis semi-classical, and the true quantum entropy, or q-entropy, which is\nachieved at the standard entanglement.\n The q-capacity, defined as the supremum over all entanglements, coincides\nwith the topological entropy. In the case of the simple algebra it doubles the\nc-capacity, coinciding with the rank-entropy. The conditional q-entropy based\non the q-entropy, is positive, unlike the von Neumann conditional entropy, and\nthe q-information of a quantum channel is proved to be additive.",
"arxiv_id": "quant-ph/0208115",
"authors": [
"V. P. Belavkin"
],
"categories": [
"quant-ph"
],
"journal_ref": "Open Sys. \u0026 Information Dyn. 8: 1-18, 2001",
"title": "On Entangled Information and Quantum Capacity",
"url": "https://arxiv.org/abs/quant-ph/0208115"
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