# Lower bounds on distances between a given quantum channel and certain classes of channels

## TL;DR

This paper derives tight lower bounds on the diamond-norm distance from a quantum channel to classes like degradable, antidegradable, and entanglement-breaking channels, using continuity bounds for quantum information measures.

## Contribution

It introduces new lower bounds on distances between quantum channels and specific classes, utilizing continuity bounds for quantum mutual information and relative entropy.

## Key findings

- Lower bounds on diamond-norm distances to degradable, antidegradable, and entanglement-breaking channels.
- Lower bounds on trace-norm distances from bipartite states to separable states.
- Establishment of tight continuity bounds for quantum information measures.

## 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.