Experimental verification of many-body entanglement using thermodynamic quantities

The phenomenon of quantum entanglement underlies several important protocols that enable emerging quantum technologies. Entangled states, however, are extremely delicate and often get perturbed by tiny fluctuations in their external environment. Certification of entanglement is therefore immensely crucial for the successful implementation of protocols involving this resource. In this Letter, we propose a set of entanglement criteria for multiqubit systems that can be easily verified by measuring certain thermodynamic quantities. In particular, the criteria depend on the difference in optimal global and local works extractable from an isolated quantum system under global and local interactions, respectively. As a proof of principle, we demonstrate the proposed scheme on nuclear spin registers of up to 10 qubits using the nuclear magnetic resonance architecture. We prepare a noisy Bell diagonal state and noisy Greenberger-Horne-Zeilinger class of states in star -topology systems and certify their entanglement through our thermodynamic criteria. Along the same line, we also propose an entanglement certification scheme in many -body systems when only partial or even no knowledge about the state is available.