dorsal/arxiv
View SchemaNew multiplicativity results for qubit maps
| Authors | Christopher King, Nilufer Koldan |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0512185 |
| URL | https://arxiv.org/abs/quant-ph/0512185 |
| DOI | 10.1063/1.2191787 |
Abstract
Let $\Phi$ be a trace-preserving, positivity-preserving (but not necessarily completely positive) linear map on the algebra of complex $2 \times 2$ matrices, and let $\Omega$ be any finite-dimensional completely positive map. For $p=2$ and $p \geq 4$, we prove that the maximal $p$-norm of the product map $\Phi \ot \Omega$ is the product of the maximal $p$-norms of $\Phi$ and $\Omega$. Restricting $\Phi$ to the class of completely positive maps, this settles the multiplicativity question for all qubit channels in the range of values $p \geq 4$.
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"abstract": "Let $\\Phi$ be a trace-preserving, positivity-preserving (but not necessarily\ncompletely positive) linear map on the algebra of complex $2 \\times 2$\nmatrices, and let $\\Omega$ be any finite-dimensional completely positive map.\nFor $p=2$ and $p \\geq 4$, we prove that the maximal $p$-norm of the product map\n$\\Phi \\ot \\Omega$ is the product of the maximal $p$-norms of $\\Phi$ and\n$\\Omega$. Restricting $\\Phi$ to the class of completely positive maps, this\nsettles the multiplicativity question for all qubit channels in the range of\nvalues $p \\geq 4$.",
"arxiv_id": "quant-ph/0512185",
"authors": [
"Christopher King",
"Nilufer Koldan"
],
"categories": [
"quant-ph"
],
"doi": "10.1063/1.2191787",
"title": "New multiplicativity results for qubit maps",
"url": "https://arxiv.org/abs/quant-ph/0512185"
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