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The verification and quantification of experimentally created entanglement bysimple measurements, especially between distant particles, is an importantbasic task in quantum processing. When composite systems are subjected to localmeasurements the measurement data will exhibit correlations, whether thesesystems are classical or quantum. Therefore, the observation of correlations inthe classical measurement record does not automatically imply the presence ofquantum correlations in the system under investigation. In this work we explorethe question of when correlations, or other measurement data, are sufficient toguarantee the existence of a certain amount of quantum correlations in thesystem and when additional information, such as the degree of purity of thesystem, is needed to do so. Various measurement settings are discussed, bothnumerically and analytically. Exact results and lower bounds on the leastentanglement consistent with the observations are presented. The approach issuitable both for the bi-partite and the multi-partite setting.Comment: 10 pages and 4 figures, material and references adde

When are correlations quantum?—verification and quantification of entanglement by simple measurements