dorsal/arxiv
View SchemaGluing of completely positive maps
| Authors | Johan Åberg |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0302182 |
| URL | https://arxiv.org/abs/quant-ph/0302182 |
| DOI | 10.1016/j.aop.2004.04.013 |
| Journal | Annals of Physics Vol. 313, p. 326 (2004) |
Abstract
Gluings of completely positive maps (CPMs) are defined and investigated. As a brief description of this concept consider a pair of `evolution machines', each with the ability to evolve the internal state of a `particle' inserted into its input. Each of these machines is characterized by a channel describing the operation the internal state has experienced when the particle is returned at the output. Suppose a particle is put in a superposition between the input of the first and the second machine. Here it is shown that the total evolution caused by a pair of such devices is not uniquely determined by the channels of the two machines. Such `global' channels describing the machine pair are examples of gluings of the two single machine channels. Under the limiting assumption that all involved Hilbert spaces are finite-dimensional, an expression which generates all subspace preserving gluings of a given pair of CPMs, is derived. The nature of the non-uniqueness of gluings and its relation to a proposed definition of subspace locality, is discussed.
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"abstract": "Gluings of completely positive maps (CPMs) are defined and investigated. As a\nbrief description of this concept consider a pair of `evolution machines\u0027, each\nwith the ability to evolve the internal state of a `particle\u0027 inserted into its\ninput. Each of these machines is characterized by a channel describing the\noperation the internal state has experienced when the particle is returned at\nthe output. Suppose a particle is put in a superposition between the input of\nthe first and the second machine. Here it is shown that the total evolution\ncaused by a pair of such devices is not uniquely determined by the channels of\nthe two machines. Such `global\u0027 channels describing the machine pair are\nexamples of gluings of the two single machine channels. Under the limiting\nassumption that all involved Hilbert spaces are finite-dimensional, an\nexpression which generates all subspace preserving gluings of a given pair of\nCPMs, is derived. The nature of the non-uniqueness of gluings and its relation\nto a proposed definition of subspace locality, is discussed.",
"arxiv_id": "quant-ph/0302182",
"authors": [
"Johan \u00c5berg"
],
"categories": [
"quant-ph"
],
"doi": "10.1016/j.aop.2004.04.013",
"journal_ref": "Annals of Physics Vol. 313, p. 326 (2004)",
"title": "Gluing of completely positive maps",
"url": "https://arxiv.org/abs/quant-ph/0302182"
},
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