Certification and quantification of the entanglement stored in a quantum memory using incomplete data

Entanglement is a main resource for various applications in quantum information processing and quantum communication. Increasing complexity of entanglement structure paves the way for both deeper fundamental tests of nature and utterly new methods for quantum information tasks. Quantum memory which is capable to store complex entanglement is essential tool for this direction since it allows to use increased quantum information capacity. Particularly, it is necessary to realize quantum repeater scheme to perform long-distance quantum communication [1]. In this context, quantum memories with high temporal multimode capacity offer a tool to realize efficient multiplexing and open a way for various applications in quantum communication studies.