dorsal/arxiv
View SchemaA Resource Framework for Quantum Shannon Theory
| Authors | I. Devetak, A. W. Harrow, A. Winter |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0512015 |
| URL | https://arxiv.org/abs/quant-ph/0512015 |
| DOI | 10.1109/TIT.2008.928980 |
| Journal | IEEE Trans. Inf. Th. vol. 54, no. 10, pp. 4587-4618, Oct 2008 |
Abstract
Quantum Shannon theory is loosely defined as a collection of coding theorems, such as classical and quantum source compression, noisy channel coding theorems, entanglement distillation, etc., which characterize asymptotic properties of quantum and classical channels and states. In this paper we advocate a unified approach to an important class of problems in quantum Shannon theory, consisting of those that are bipartite, unidirectional and memoryless. We formalize two principles that have long been tacitly understood. First, we describe how the Church of the larger Hilbert space allows us to move flexibly between states, channels, ensembles and their purifications. Second, we introduce finite and asymptotic (quantum) information processing resources as the basic objects of quantum Shannon theory and recast the protocols used in direct coding theorems as inequalities between resources. We develop the rules of a resource calculus which allows us to manipulate and combine resource inequalities. This framework simplifies many coding theorem proofs and provides structural insights into the logical dependencies among coding theorems. We review the above-mentioned basic coding results and show how a subset of them can be unified into a family of related resource inequalities. Finally, we use this family to find optimal trade-off curves for all protocols involving one noisy quantum resource and two noiseless ones.
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"abstract": "Quantum Shannon theory is loosely defined as a collection of coding theorems,\nsuch as classical and quantum source compression, noisy channel coding\ntheorems, entanglement distillation, etc., which characterize asymptotic\nproperties of quantum and classical channels and states. In this paper we\nadvocate a unified approach to an important class of problems in quantum\nShannon theory, consisting of those that are bipartite, unidirectional and\nmemoryless.\n We formalize two principles that have long been tacitly understood. First, we\ndescribe how the Church of the larger Hilbert space allows us to move flexibly\nbetween states, channels, ensembles and their purifications. Second, we\nintroduce finite and asymptotic (quantum) information processing resources as\nthe basic objects of quantum Shannon theory and recast the protocols used in\ndirect coding theorems as inequalities between resources. We develop the rules\nof a resource calculus which allows us to manipulate and combine resource\ninequalities. This framework simplifies many coding theorem proofs and provides\nstructural insights into the logical dependencies among coding theorems.\n We review the above-mentioned basic coding results and show how a subset of\nthem can be unified into a family of related resource inequalities. Finally, we\nuse this family to find optimal trade-off curves for all protocols involving\none noisy quantum resource and two noiseless ones.",
"arxiv_id": "quant-ph/0512015",
"authors": [
"I. Devetak",
"A. W. Harrow",
"A. Winter"
],
"categories": [
"quant-ph"
],
"doi": "10.1109/TIT.2008.928980",
"journal_ref": "IEEE Trans. Inf. Th. vol. 54, no. 10, pp. 4587-4618, Oct 2008",
"title": "A Resource Framework for Quantum Shannon Theory",
"url": "https://arxiv.org/abs/quant-ph/0512015"
},
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