# Asymptotic properties of entanglement polytopes for large number of qubits

## TL;DR

This paper investigates the asymptotic behavior of entanglement polytopes in large qubit systems, revealing limitations in their ability to distinguish entanglement classes as the number of qubits grows.

## Contribution

It provides the first asymptotic analysis of entanglement polytopes, showing their accumulation near maximally mixed states and highlighting inherent limitations in entanglement witnessing for large systems.

## Key findings

- Entanglement polytopes cluster near maximally mixed states as qubits increase.
- Overlap of many polytopes reduces their effectiveness in entanglement detection.
- Witnessing power cannot be improved by entanglement distillation in large systems.

## Abstract

Entanglement polytopes have been recently proposed as the way of witnessing the SLOCC multipartite entanglement classes using single particle information. We present first asymptotic results concerning feasibility of this approach for large number of qubits. In particular we show that entanglement polytopes of $L$-qubit system accumulate in the distance $\frac{1}{2\sqrt{L}}$ from the point corresponding to the maximally mixed reduced one-qubit density matrices. This implies existence of a possibly large region where many entanglement polytopes overlap, i.e where the witnessing power of entanglement polytopes is weak. Moreover, the witnessing power cannot be strengthened by any entanglement distillation protocol as for large $L$ the required purity is above current capability.