Deciding whether a mixed state of a quantum system is entangled or not is a notoriously difficult problem. In the paper published in Quantum, our colleagues Szilárd Szalay and Géza Tóth presented new one-parameter multipartite entanglement properties, and the corresponding metrological criteria qualifying these.
In a nutshell the new criterion formulates that good metrological precision, quantified by the quantum Fisher information, indicates that the average size of entangled subsystems is high. This is much stronger than the criterion known earlier, which gives a lower bound on the size of the largest entangled subsystem, not taking into account its possibly small weight in the mixture. Such metrological criteria are rather useful, since the quantum Fisher information can be calculated if the quantum state is known, or it can be bounded from below in measurements without the knowledge (tomography) of the state, which would be infeasible even for not too large quantum systems.
keywords: quantum entanglement, multipartite entanglement, entanglement criteria, entanglement depth, quantum metrology, quantum Fisher information
