# Entanglement distance for an arbitrary state of M qubits

## TL;DR

This paper introduces a novel entanglement measure for pure states of M-qubit systems based on a distance derived from the Fubini-Study metric, which is invariant under local unitaries and provides insights into entanglement robustness.

## Contribution

It proposes a new entanglement measure as a distance derived from the Fubini-Study metric, applicable to any pure M-qubit state, and analyzes its eigenvalues for robustness insights.

## Key findings

- The measure is invariant under local unitary transformations.
- Eigenvalues of the entanglement metric relate to entanglement robustness.
- The measure can be computed for any pure M-qubit state.

## Abstract

We propose a measure of entanglement that can be computed for any pure state of an $M$-qubit system. The entanglement measure has the form of a distance that we derive from an adapted application of the Fubini-Study metric. This measure is invariant under local unitary transformations and defined as trace of a suitable metric that we derive, the entanglement metric $\tilde{g}$. Furthermore, the analysis of the eigenvalues of $\tilde{g}$ gives information about the robustness of entanglement.