Geodesic
Complementary channels and the additivity problem
Teoriâ veroâtnostej i ee primeneniâ, Tome 51 (2006) no. 1, pp. 133-143

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We explore the complementarity between output and environment of a quantum channel (or, more generally, completely positive (CP) map), making an observation that the output purity characteristics for complementary CP maps coincide. Hence, the validity of the mutiplicativity/additivity conjecture for a class of CP maps implies its validity for complementary maps. The class of CP maps complementary to entanglement-breaking ones is described and is shown to contain diagonal CP maps as a proper subclass, resulting in a new class of CP maps (channels) for which the multiplicativity/additivity holds. Covariant and Gaussian channels are discussed briefly in this context.
Keywords: quantum channel, completely positive map, additivity conjecture. 
@article{TVP_2006_51_1_a9,
     author = {A. S. Holevo},
     title = {Complementary channels and the additivity problem},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {133--143},
     publisher = {mathdoc},
     volume = {51},
     number = {1},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2006_51_1_a9/}
}
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A. S. Holevo. Complementary channels and the additivity problem. Teoriâ veroâtnostej i ee primeneniâ, Tome 51 (2006) no. 1, pp. 133-143. http://geodesic.mathdoc.fr/item/TVP_2006_51_1_a9/