dorsal/arxiv
View SchemaAn Analysis of Completely-Positive Trace-Preserving Maps on 2x2 Matrices
| Authors | Mary Beth Ruskai, Stanislaw Szarek, Elisabeth Werner |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0101003 |
| URL | https://arxiv.org/abs/quant-ph/0101003 |
| Journal | Lin. Alg. Appl. 347, 159--187 (2002) |
Abstract
We give a useful new characterization of the set of all completely positive, trace-preserving (i.e., stochastic) maps from 2x2 matrices to 2x2 matrices. These conditions allow one to easily check any trace-preserving map for complete positivity. We also determine explicitly all extreme points of this set, and give a useful parameterization after reduction to a certain canonical form. This allows a detailed examination of an important class of non-unital extreme points which can be characterized as having exactly two images on the Bloch sphere. We also discuss a number of related issues about the images and the geometry of the set of stochastic maps, and show that any stochastic map on 2x2 matrices can be written as a convex combination of two "generalized" extreme points.
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"abstract": "We give a useful new characterization of the set of all completely positive,\ntrace-preserving (i.e., stochastic) maps from 2x2 matrices to 2x2 matrices.\nThese conditions allow one to easily check any trace-preserving map for\ncomplete positivity. We also determine explicitly all extreme points of this\nset, and give a useful parameterization after reduction to a certain canonical\nform. This allows a detailed examination of an important class of non-unital\nextreme points which can be characterized as having exactly two images on the\nBloch sphere.\n We also discuss a number of related issues about the images and the geometry\nof the set of stochastic maps, and show that any stochastic map on 2x2 matrices\ncan be written as a convex combination of two \"generalized\" extreme points.",
"arxiv_id": "quant-ph/0101003",
"authors": [
"Mary Beth Ruskai",
"Stanislaw Szarek",
"Elisabeth Werner"
],
"categories": [
"quant-ph",
"math-ph",
"math.MP",
"math.OA",
"math.RA"
],
"journal_ref": "Lin. Alg. Appl. 347, 159--187 (2002)",
"title": "An Analysis of Completely-Positive Trace-Preserving Maps on 2x2 Matrices",
"url": "https://arxiv.org/abs/quant-ph/0101003"
},
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