# Entanglement Measures in Embedding Quantum Simulators with Nuclear Spins

## TL;DR

This paper demonstrates an embedding quantum simulator using nuclear spins to efficiently measure entanglement in multi-qubit systems, significantly reducing measurement complexity.

## Contribution

It introduces a nuclear spin-based EQS that efficiently measures entanglement measures like concurrence and three-tangle with fewer measurements.

## Key findings

- Successfully implemented a 3-qubit EQS with an ancillary qubit.
- Achieved efficient entanglement measurement reducing full-state tomography.
- Utilized NMR techniques on trans-crotonic acid molecules.

## Abstract

We implement an embedding quantum simulator (EQS) in nuclear spin systems. The experiment consists of a simulator of up to three qubits, plus a single ancillary qubit, where we are able to efficiently measure the concurrence and the three-tangle of two-qubit and a three-qubit systems as they undergo entangling dynamics. The EQS framework allows us to drastically reduce the number of measurements needed for this task, which otherwise would require full-state reconstruction of the qubit system. Our simulator is built of the nuclear spins of 4 $^{13}C$ atoms in a molecule of trans-crotonic acid manipulated with NMR techniques.