dorsal/arxiv
View SchemaNotes on super-operator norms induced by Schatten norms
| Authors | John Watrous |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0411077 |
| URL | https://arxiv.org/abs/quant-ph/0411077 |
Abstract
This paper considers basic properties of super-operator norms induced by Schatten p-norms. Such super-operator norms arise in various contexts in the study of quantum information. It is proved that for completely positive super-operators, the value of any such norm is achieved by a positive semidefinite input, answering a question recently posed by King and Ruskai. However, for any choice of p, there exists a super-operator that is the difference of two completely positive, trace-preserving super-operators such that the value of the super-operator norm is not even achieved on a Hermitian input operator. Also considered are the properties of the above norms for super-operators tensored with the identity super-operator.
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"abstract": "This paper considers basic properties of super-operator norms induced by\nSchatten p-norms. Such super-operator norms arise in various contexts in the\nstudy of quantum information. It is proved that for completely positive\nsuper-operators, the value of any such norm is achieved by a positive\nsemidefinite input, answering a question recently posed by King and Ruskai.\nHowever, for any choice of p, there exists a super-operator that is the\ndifference of two completely positive, trace-preserving super-operators such\nthat the value of the super-operator norm is not even achieved on a Hermitian\ninput operator. Also considered are the properties of the above norms for\nsuper-operators tensored with the identity super-operator.",
"arxiv_id": "quant-ph/0411077",
"authors": [
"John Watrous"
],
"categories": [
"quant-ph"
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"title": "Notes on super-operator norms induced by Schatten norms",
"url": "https://arxiv.org/abs/quant-ph/0411077"
},
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