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

TL;DR

This paper introduces a new geometric entanglement measure for N-qubit pure and mixed states based on the correlation tensor norm, demonstrating its properties and applications in quantum algorithms and many-body systems.

Contribution

It proposes a novel entanglement measure using the correlation tensor norm, extending it to mixed states, and validates its properties and usefulness in various quantum contexts.

Findings

The measure accurately quantifies entanglement in GHZ and W states.

It tracks entanglement dynamics in Grover's algorithm.

The measure is proven to be monotonic and additive for mixed states.

Abstract

We present a multipartite entanglement measure for $N$-qubit pure states, using the norm of the correlation tensor which occurs in the Bloch representation of the state. We compute this measure for several important classes of $N$-qubit pure states such as GHZ states, W states and their superpositions. We compute this measure for interesting applications like one dimensional Heisenberg antiferromagnet. We use this measure to follow the entanglement dynamics of Grover's algorithm. We prove that this measure possesses almost all the properties expected of a good entanglement measure, including monotonicity. Finally, we extend this measure to $N$-qubit mixed states via convex roof construction and establish its various properties, including its monotonicity. We also introduce a related measure which has all properties of the above measure and is also additive.