Experimentally characterizing multiparticle entanglement based on measuring quantum Fisher information

Abstract

Quantum Fisher information plays a vital role in the field of quantum metrology and quantum information, because it not only quantifies the ultimate precision bound of parameter estimation but also provides criteria for entanglement detection. Nevertheless, experimentally extracting quantum Fisher information is intractable. Quantum state tomography is a typical approach to obtaining the complete information about a quantum system and extract quantum Fisher information. However it becomes infeasible for large-scale quantum systems owing to the exponentially growing complexity. In this paper, we present a general relationship between quantum Fisher information and the overlap of quantum states. Specifically, we show that for pure states, the quantum Fisher information can be exactly extracted from the overlap, whereas for mixed states, only the lower bound can be obtained. We also develop a protocol for measuring the overlap of quantum states, which only requires one additional auxiliary qubit and a single measurement for pure state. Our protocol is more efficient and scalable than previous approaches because it requires less time and fewer measurements. We use this protocol to characterize the multiparticle entanglement in a three-body interaction system undergoing adiabatic quantum phase transition, and experimentally demonstrate its feasibility for the first time in a nuclear magnetic resonance quantum system. We conduct our experiment on a 4-qubit nuclear magnetic resonance quantum simulator, three of which are used to simulate the quantum phase transition in a three-body interaction system, and the remaining one is used as the auxiliary qubit to detect the overlap of the quantum state. We use gradient ascent pulse engineering pulses to implement the process of evolution. By measuring the auxiliary qubit, the experimental results of quantum Fisher information are obtained and match well with the theoretical predictions, thus successfully characterizing the multiparticle entanglement in a practical quantum system. We further confirm our results by performing quantum state tomography on some quantum states in the adiabatic process. The experimentally reconstructed quantum states are close to the corresponding instantaneous ground states.