# Bounds on Negativity of Superpositions

## TL;DR

This paper investigates the negativity of superposed pure bipartite states, establishing bounds and continuity properties of entanglement measures like concurrence, with implications for estimating entanglement in quantum systems.

## Contribution

It provides new bounds on negativity for superposed states and demonstrates the continuity of concurrence even in infinite-dimensional systems.

## Key findings

- High fidelity states have nearly the same entanglement.
- Bounds on negativity are derived in terms of component states.
- Concurrence is shown to be a continuous function in infinite dimensions.

## Abstract

The entanglement quantified by negativity of pure bipartite superposed states is studied. We show that if the entanglement is quantified by the concurrence two pure states of high fidelity to one another still have nearly the same entanglement. Furthermore this conclusion can be guaranteed by our obtained inequality, and the concurrence is shown to be a continuous function even in infinite dimensions. The bounds on the negativity of superposed states in terms of those of the states being superposed are obtained. These bounds can find useful applications in estimating the amount of the entanglement of a given pure state.