Geodesic
Lower estimates for distances from a given quantum channel to certain classes of quantum channels
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Quantum computing, Tome 138 (2017), pp. 125-131.

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By using estimates for the variation of quantum mutual information and the relative entropy of entanglement, we obtain $\varepsilon$-exact lower estimates for distances from a given quantum channels to sets of degraded, anti-degraded, and entanglement-breaking channels. As an auxiliary result, we obtain $\varepsilon$-exact lower estimates for the distance from a given two-particle state to the set of all separable states.
Keywords: quantum state, quantum channel, coherent information, separable states, relative entropy of entanglement. 
@article{INTO_2017_138_a8,
     author = {M. E. Shirokov and A. V. Bulinski},
     title = {Lower estimates for distances from a given quantum channel to  certain classes of quantum channels},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {125--131},
     publisher = {mathdoc},
     volume = {138},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2017_138_a8/}
}
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M. E. Shirokov; A. V. Bulinski. Lower estimates for distances from a given quantum channel to  certain classes of quantum channels. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Quantum computing, Tome 138 (2017), pp. 125-131. http://geodesic.mathdoc.fr/item/INTO_2017_138_a8/