Lower bounds on distances between a given quantum channel and certain classes of channels
arXiv:1705.04223 · doi:10.1007/s10958-019-04419-2
Abstract
The tight, in a sense, lower estimates of diamond-norm distance from a given quantum channel to the sets of degradable, antidegradable and entanglement-breaking channels are obtained via the tight continuity bounds for quantum mutual information and for relative entropy of entanglement in finite-dimensional case. As an auxiliary result there are established lower bounds of trace-norm distance from a given bipartite state to the set of all separable states.
12 pages