# Absolutely separating quantum maps and channels

## TL;DR

This paper investigates the properties of absolutely separating quantum maps and channels, showing their effects on quantum states and their relation to entanglement, with implications for quantum information processing.

## Contribution

It introduces the concept of absolutely separating maps, analyzes their properties, and explores their stability and behavior in multipartite quantum systems.

## Key findings

- Absolutely separating maps are not necessarily entanglement breaking.
- The tensor product of an absolutely separating map is only absolutely separating if it is the tracing map.
- Certain local and global channels can produce absolutely separable states under specific conditions.

## Abstract

Absolutely separable states $\varrho$ remain separable under arbitrary unitary transformations $U \varrho U^{\dag}$. By example of a three qubit system we show that in multipartite scenario neither full separability implies bipartite absolute separability nor the reverse statement holds. The main goal of the paper is to analyze quantum maps resulting in absolutely separable output states. Such absolutely separating maps affect the states in a way, when no Hamiltonian dynamics can make them entangled afterwards. We study general properties of absolutely separating maps and channels with respect to bipartitions and multipartitions and show that absolutely separating maps are not necessarily entanglement breaking. We examine stability of absolutely separating maps under tensor product and show that $\Phi^{\otimes N}$ is absolutely separating for any $N$ if and only if $\Phi$ is the tracing map. Particular results are obtained for families of local unital multiqubit channels, global generalized Pauli channels, and combination of identity, transposition, and tracing maps acting on states of arbitrary dimension. We also study the interplay between local and global noise components in absolutely separating bipartite depolarizing maps and discuss the input states with high resistance to absolute separability.