Entanglement detection

Zhenhuan Liu, Fuchuan Wei

Entanglement detection is one of the most fundamental tasks in quantum information science, playing vital roles in theoretical studies and quantum system benchmarking. Researchers have proposed many powerful entanglement criteria with high detection capabilities and small observable numbers. Nonetheless, entanglement criteria only represent mathematical rules deciding the existence of entanglement. The relationship between a good entanglement criterion and an effective experimental entanglement detection protocol (EDP) is poorly understood. In this study, we introduce postulates for EDPs about their detection capabilities and robustness and use them to show the difference between entanglement criteria and EDPs. Specifically, we design an entanglement detection task for unknown pure bipartite states and demonstrate that the sample complexity of any EDP and the number of observables for a good entanglement criterion can have exponential separation. Furthermore, we discover that the optimal EDP with the lowest sample complexity does not necessarily correspond to an entanglement criterion constructed by a small number of observables. Our results can be used to prove the exponential speedups achieved through quantum memory and be generalized to multipartite entanglement detection. By highlighting the significance and independence of EDP design, our work holds practical implications for entanglement detection experiments.

Dagmar Bruβ

Yiding Wang, Tinggui Zhang, Xiaofen Huang +1 more

We present a nonlinear entanglement detection strategy that detects entanglement that the linear detection strategy fails. We show that when the nonlinear entanglement detection strategy fails to detect the entanglement of an entangled state with two copies, it may succeed with three or more copies. Based on our strategy, a witness combined with a suitable quantum mechanical observable may detect the entanglement that cannot be detected by the witness alone. Moreover, our strategy can also be applied to detect multipartite entanglement by using the witnesses for bipartite systems, as well as to entanglement concentrations.

Barbara M. Terhal

Fei Shi, Lin Chen, Giulio Chiribella +1 more

Multipartite entanglement is a valuable resource for quantum technologies. However, detecting this resource can be challenging: for genuine multipartite entanglement, the detection may require global measurements that are hard to implement experimentally. Here we introduce the concept of entanglement detection length, defined as the minimum number of particles that have to be jointly measured in order to detect genuine multipartite entanglement. For symmetric states, we show that the entanglement detection length can be determined by testing separability of the marginal states. For general states, we provide an upper bound on the entanglement detection length based on semidefinite programming. We show that the entanglement detection length is generally smaller than the minimum observable length needed to uniquely determine a multipartite state, and we provide examples achieving the maximum gap between these two quantities.