1983
DOI: 10.2307/2044351
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Tracial Positive Linear Maps of C ∗ -Algebras

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Cited by 33 publications
(51 citation statements)
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“…Completely positive maps find direct application in quantum theory as they correspond to quantum operations, which can be realized in a physical experiment. On the other hand, in spite of a considerable effort several years ago [1][2][3][4][5][6][7][8][9][10][11][12][13][14] and more recently [15][16][17][18][19][20][21][22][23][24] the structure of the set of positive maps acting on operators defined on a d dimensional Hilbert space H d is well understood only for d = 2. In this case every positive map is decomposable, as it can be represented as a sum of a completely positive map and a completely co-positive map.…”
Section: Introductionmentioning
confidence: 99%
“…Completely positive maps find direct application in quantum theory as they correspond to quantum operations, which can be realized in a physical experiment. On the other hand, in spite of a considerable effort several years ago [1][2][3][4][5][6][7][8][9][10][11][12][13][14] and more recently [15][16][17][18][19][20][21][22][23][24] the structure of the set of positive maps acting on operators defined on a d dimensional Hilbert space H d is well understood only for d = 2. In this case every positive map is decomposable, as it can be represented as a sum of a completely positive map and a completely co-positive map.…”
Section: Introductionmentioning
confidence: 99%
“…Choi [3] realized that (32) and (33) hold under the weaker condition that Φ is 2-positive. His approach is quite different, and based on the fact that a 2 × 2 block matrix P C C † Q is positive semi-definite if and only if C = √ P X √ Q with X a contraction, i.e., X † X ≤ I.…”
Section: Schwarz Inequalities For Cp Mapsmentioning
confidence: 99%
“…The most general form of such a dependence is by a dynamical map [1]: The Hermitian super matrix B is not necessarily positive. If it is, then B is said to be completely positive [2]. We note that unitary evolution is of this form with one single nonzero eigenvalue:…”
Section: Stochastic Dynamics Of Open Systemsmentioning
confidence: 99%