Experimental Verification of Many-Body Entanglement Using Thermodynamic Quantities

The phenomenon of quantum entanglement underlies several important protocolsthat enable emerging quantum technologies. Entangled states, however, areextremely delicate and often get perturbed by tiny fluctuations in theirexternal environment. Certification of entanglement is therefore immenselycrucial for the successful implementation of protocols involving this resource.In this work, we propose a set of entanglement criteria for multi-qubit systemsthat can be easily verified by measuring certain thermodynamic quantities. Inparticular, the criteria depend on the difference in optimal global and localworks extractable from an isolated quantum system under global and localinteractions, respectively. As a proof of principle, we demonstrate theproposed scheme on nuclear spin registers of up to 10 qubits using the NuclearMagnetic Resonance architecture. We prepare noisy Bell-diagonal state and noisyGreenberger-Horne-Zeilinger class of states in star-topology systems andcertify their entanglement through our thermodynamic criteria. Along the sameline, we also propose an entanglement certification scheme in many-body systemswhen only partial or even no knowledge about the state is available.