Computable and Operationally Meaningful Multipartite Entanglement Measures

Multipartite entanglement is an essential resource for quantum communication, quantum computing, quantum sensing, and quantum networks. The utility of a quantum state vertical bar psi > for these applications is often directly related to the degree or type of entanglement present in vertical bar psi >. Therefore, efficiently quantifying and characterizing multipartite entanglement is of paramount importance. In this work, we introduce a family of multipartite entanglement measures, called concentratable entanglements. Several well-known entanglement measures are recovered as special cases of our family of measures, and hence we provide a general framework for quantifying multipartite entanglement. We prove that the entire family does not increase, on average, under local operations and classical communications. We also provide an operational meaning for these measures in terms of probabilistic concentration of entanglement into Bell pairs. Finally, we show that these quantities can be efficiently estimated on a quantum computer by implementing a parallelized SWAP test, opening up a research direction for measuring multipartite entanglement on quantum devices.

Automated summary

In this work, a family of multipartite entanglement measures called concentratable entanglements is introduced, providing a general framework for quantifying multipartite entanglement. These measures do not increase, on average, under local operations and classical communications, and have an operational meaning in terms of probabilistic concentration of entanglement into Bell pairs. Furthermore, these measures can be efficiently estimated on a quantum computer through a parallelized SWAP test, paving the way for measuring multipartite entanglement on quantum devices.