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Published in 2021 at "Communications in Mathematical Physics"
DOI: 10.1007/s00220-021-04245-1
Abstract: We study the quantum ($C^*$) convexity structure of normalized positive operator valued measures (POVMs) on measurable spaces. In particular, it is seen that unlike extreme points under classical convexity, $C^*$-extreme points of normalized POVMs on…
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Keywords:
unital completely;
valued measures;
operator valued;
extreme points ... See more keywords
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Published in 2018 at "Central European Journal of Operations Research"
DOI: 10.1007/s10100-017-0499-2
Abstract: A symmetric matrix of order n is called completely positive if it has a symmetric factorization by means of a rectangular matrix with n columns and no negative entries (a so-called cp factorization), i.e., if…
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Keywords:
dimension;
positive factorization;
factorization;
matrix ... See more keywords
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Published in 2021 at "Israel Journal of Mathematics"
DOI: 10.1007/s11856-021-2198-x
Abstract: We examine a special case of an approximation of the joint spectral radius given by Blondel and Nesterov, which we call the outer spectral radius. The outer spectral radius is given by the square root…
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Keywords:
spectral radius;
radius;
outer spectral;
completely positive ... See more keywords
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Published in 2020 at "Linear Algebra and its Applications"
DOI: 10.1016/j.laa.2019.12.024
Abstract: Abstract A matrix A is called completely positive, if there exists an entrywise nonnegative matrix B such that A = B B T . These matrices play a major role in combinatorial and quadratic optimization.…
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Keywords:
factorization method;
positive matrices;
method completely;
method ... See more keywords
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Published in 2018 at "Journal of Mathematical Physics"
DOI: 10.1063/1.5027616
Abstract: Completely positive maps are useful in modeling the discrete evolution of quantum systems. Spectral properties of operators associated with such maps are relevant for determining the asymptotic dynamics of quantum systems subjected to multiple interactions…
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Keywords:
quantum;
quantum systems;
asymptotic dynamics;
shemesh theorem ... See more keywords
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Published in 2019 at "Physical Review A"
DOI: 10.1103/physreva.100.012336
Abstract: We show that the set of not-completely-positive (NCP) maps is unbounded, unless further assumptions are made. This is done by first proposing a reasonable definition of a valid NCP map, which is nontrivial because NCP…
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Keywords:
measure completely;
qubit maps;
completely positive;
ncp maps ... See more keywords
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Published in 2019 at "Physical Review A"
DOI: 10.1103/physreva.99.052352
Abstract: Valid transformations between quantum states are necessarily described by completely positive maps, instead of just positive maps. Positive but not completely positive maps such as the transposition map cannot be implemented due to the existence…
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Keywords:
positive maps;
copies input;
completely positive;
input state ... See more keywords
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Published in 2020 at "Forum Mathematicum"
DOI: 10.1515/forum-2020-0012
Abstract: Abstract We extend the definition of order zero maps to the setting of pro-C*{C^{*}}-algebras and generalize structure theorems of order zero maps between C*{C^{*}}-algebras to strongly bounded order zero maps between pro-Cβ{C^{\ast}}-algebras. An application to…
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Keywords:
zero maps;
order;
pro algebras;
positive maps ... See more keywords