An Experimentally accessible geometric measure for entanglement in $N$-qudit pure states

TL;DR

This paper introduces a new geometric entanglement measure for N-qudit pure states based on the correlation tensor norm, demonstrating its properties and extending it to mixed states.

Contribution

It proposes a novel multipartite entanglement measure using the correlation tensor norm and extends it to mixed states, with proven monotonicity and other desirable properties.

Findings

The measure is computed explicitly for N-qutrit GHZ states.

The measure satisfies key properties of a good entanglement measure, including monotonicity.

Extension to mixed states via convex roof maintains these properties.

Abstract

We present a multipartite entanglement measure for $N$-qudit pure states, using the norm of the correlation tensor which occurs in the Bloch representation of the state. We compute this measure for important class of $N$-qutrit pure states, namely general GHZ states. We prove that this measure possesses almost all the properties expected of a good entanglement measure, including monotonicity. Finally, we extend this measure to $N$-qudit mixed states via convex roof construction and establish its various properties, including its monotonicity.