  The quantum states built with the eta paring mechanism i.e., eta pairing
states, were first introduced in the context of high temperature
superconductivity where they were recognized as important example of states
allowing for off-diagonal long-range order (ODLRO). In this paper we describe
the structure of the correlations present in these states when considered in
their momentum representation and we explore the relations between the quantum
bipartite/multipartite correlations exhibited in k space and the direct lattice
superconducting correlations. In particular, we show how the negativity between
paired momentum modes is directly related to the ODLRO. Moreover, we
investigate the dependence of the block entanglement on the choice of the modes
forming the block and on the ODLRO; consequently we determine the multipartite
content of the entanglement through the evaluation of the generalized "Meyer
Wallach" measure in the direct and reciprocal lattice. The determination of the
persistency of entanglement shows how the network of correlations depicted
exhibits a self-similar structure which is robust with respect to "local"
measurements. Finally, we recognize how a relation between the momentum-space
quantum correlations and the ODLRO can be established even in the case of BCS
states.
