Accessible quantification of multiparticle entanglement

TL;DR

This paper introduces a practical method for quantifying multiparticle entanglement in quantum systems, providing analytical results and bounds that require minimal measurements, facilitating experimental assessment of entanglement.

Contribution

It develops an experimentally feasible approach to evaluate geometric measures of multiparticle entanglement, including analytical results and bounds applicable to general states.

Findings

Provides analytical results for specific mixed states of N qubits.

Offers computable lower bounds for global, partial, and genuine multiparticle entanglement.

Requires only three local measurement settings for global and partial entanglement estimation.

Abstract

Entanglement is a key ingredient for quantum technologies and a fundamental signature of quantumness in a broad range of phenomena encompassing many-body physics, thermodynamics, cosmology, and life sciences. For arbitrary multiparticle systems, entanglement quantification typically involves nontrivial optimisation problems, and may require demanding tomographical techniques. Here we develop an experimentally feasible approach to the evaluation of geometric measures of multiparticle entanglement. Our approach provides analytical results for particular classes of mixed states of N qubits, and computable lower bounds to global, partial, or genuine multiparticle entanglement of any general state. For global and partial entanglement, useful bounds are obtained with minimum effort, requiring local measurements in just three settings for any N. For genuine entanglement, a number of measurements scaling linearly with N is required. We demonstrate the power of our approach to estimate and quantify different types of multiparticle entanglement in a variety of N-qubit states useful for quantum information processing and recently engineered in laboratories with quantum optics and trapped ion setups.