dorsal/arxiv
View SchemaA triangle of dualities: reversibly decomposable quantum channels, source-channel duality, and time reversal
| Authors | I. Devetak |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0505138 |
| URL | https://arxiv.org/abs/quant-ph/0505138 |
| DOI | 10.1103/PhysRevLett.97.140503 |
Abstract
Two quantum information processing protocols are said to be dual under resource reversal if the resources consumed (generated) in one protocol are generated (consumed) in the other. Previously known examples include the duality between entanglement concentration and dilution, and the duality between coherent versions of teleportation and super-dense coding. A quantum feedback channel is an isometry from a system belonging to Alice to a system shared between Alice and Bob. We show that such a resource may be reversibly decomposed into a perfect quantum channel and pure entanglement, generalizing both of the above examples. The dual protocols responsible for this decomposition are the ``feedback father'' (FF) protocol and the ``fully quantum reverse Shannon'' (FQRS) protocol. Moreover, the ``fully quantum Slepian-Wolf'' protocol (FQSW), a generalization of the recently discovered ``quantum state merging'', is related to FF by source-channel duality, and to FQRS by time reversal duality, thus forming a triangle of dualities. The source-channel duality is identified as the origin of the previously poorly understood ``mother-father'' duality. Due to a symmetry breaking, the dualities extend only partially to classical information theory.
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"abstract": "Two quantum information processing protocols are said to be dual under\nresource reversal if the resources consumed (generated) in one protocol are\ngenerated (consumed) in the other. Previously known examples include the\nduality between entanglement concentration and dilution, and the duality\nbetween coherent versions of teleportation and super-dense coding. A quantum\nfeedback channel is an isometry from a system belonging to Alice to a system\nshared between Alice and Bob. We show that such a resource may be reversibly\ndecomposed into a perfect quantum channel and pure entanglement, generalizing\nboth of the above examples. The dual protocols responsible for this\ndecomposition are the ``feedback father\u0027\u0027 (FF) protocol and the ``fully quantum\nreverse Shannon\u0027\u0027 (FQRS) protocol. Moreover, the ``fully quantum Slepian-Wolf\u0027\u0027\nprotocol (FQSW), a generalization of the recently discovered ``quantum state\nmerging\u0027\u0027, is related to FF by source-channel duality, and to FQRS by time\nreversal duality, thus forming a triangle of dualities. The source-channel\nduality is identified as the origin of the previously poorly understood\n``mother-father\u0027\u0027 duality. Due to a symmetry breaking, the dualities extend\nonly partially to classical information theory.",
"arxiv_id": "quant-ph/0505138",
"authors": [
"I. Devetak"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevLett.97.140503",
"title": "A triangle of dualities: reversibly decomposable quantum channels, source-channel duality, and time reversal",
"url": "https://arxiv.org/abs/quant-ph/0505138"
},
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