# Entanglement increase from local interactions with not-completely-positive maps

## TL;DR

This paper demonstrates that local interactions with non-completely-positive maps can both increase and decrease entanglement between two qubits, challenging traditional assumptions about entanglement dynamics.

## Contribution

It provides explicit examples showing entanglement can be increased by local interactions involving non-completely-positive maps, revealing new dynamics in quantum entanglement.

## Key findings

- Entanglement can be increased by local interactions with non-CP maps.
- Entanglement decay can be non-exponential, reaching zero at finite time.
- Local interactions with a control qubit can alter entanglement without direct interaction.

## Abstract

Simple examples are constructed that show the entanglement of two qubits being both increased and decreased by interactions on just one of them. One of the two qubits interacts with a third qubit, a control, that is never entangled or correlated with either of the two entangled qubits and is never entangled, but becomes correlated, with the system of those two qubits. The two entangled qubits do not interact, but their state can change from maximally entangled to separable or from separable to maximally entangled. Similar changes for the two qubits are made with a swap operation between one of the qubits and a control; then there are compensating changes of entanglement that involve the control. When the entanglement increases, the map that describes the change of the state of the two entangled qubits is not completely positive. Combination of two independent interactions that individually give exponential decay of the entanglement can cause the entanglement to not decay exponentially but, instead, go to zero at a finite time.