  The notion of "paired" fermions is central to important condensed matter
phenomena such as superconductivity and superfluidity. While the concept is
widely used and its physical meaning is clear there exists no systematic and
mathematical theory of pairing which would allow to unambiguously characterize
and systematically detect paired states. We propose a definition of pairing and
develop methods for its detection and quantification applicable to current
experimental setups. Pairing is shown to be a quantum correlation different
from entanglement, giving further understanding in the structure of highly
correlated quantum systems. In addition, we will show the resource character of
paired states for precision metrology, proving that the BCS states allow phase
measurements at the Heisenberg limit.
