$$C^*$$-Extreme Points of Positive Operator Valued Measures and Unital Completely Positive Maps
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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… read more here.
Keywords: unital completely; valued measures; operator valued; extreme points ... See more keywords
Building a completely positive factorization
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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… read more here.
Keywords: dimension; positive factorization; factorization; matrix ... See more keywords
The outer spectral radius and dynamics of completely positive maps
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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… read more here.
Keywords: spectral radius; radius; outer spectral; completely positive ... See more keywords
A factorization method for completely positive matrices
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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.… read more here.
Keywords: factorization method; positive matrices; method completely; method ... See more keywords
Application of Shemesh theorem to quantum channels
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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… read more here.
Keywords: quantum; quantum systems; asymptotic dynamics; shemesh theorem ... See more keywords
Measure of not-completely-positive qubit maps: The general case
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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… read more here.
Keywords: measure completely; qubit maps; completely positive; ncp maps ... See more keywords
Implementing positive maps with multiple copies of an input state
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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… read more here.
Keywords: positive maps; copies input; completely positive; input state ... See more keywords
Completely positive maps of order zero on pro-πΆβ-algebras
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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… read more here.
Keywords: zero maps; order; pro algebras; positive maps ... See more keywords