Bounding the entanglement of N qubits with only four measurements

TL;DR

This paper presents a new method to quantify the genuine N-partite entanglement of N-qubit states using only four measurements, enabling efficient bounds on entanglement in experimental GHZ states.

Contribution

Introduces a trace distance-based measure for N-partite entanglement and derives an algebraic formula for GHZ-diagonal states, reducing measurement complexity.

Findings

Provides a practical bound on all-party entanglement with minimal measurements

Derives an explicit algebraic formula for GHZ-diagonal states

Demonstrates applicability to experimentally produced GHZ states

Abstract

We introduce a new measure for the genuinely N-partite (all-party) entanglement of N-qubit states using the trace distance metric, and find an algebraic formula for the GHZ-diagonal states. We then use this formula to show how the all-party entanglement of experimentally produced GHZ states of an arbitrary number of qubits may be bounded with only four measurements.