  We propose an approach for collective enhancement of precision for remotely
located optical lattice clocks and a way of generation of the
Einstein-Podolsky-Rosen state of remote clocks. Close to Heisenberg scaling of
the clock precision with the number of clocks M can be achieved even for an
optical channel connecting clocks with substantial losses. This scenario
utilizes a collective quantum nondemolition measurement on clocks with parallel
Bloch vectors for enhanced measurement precision. We provide an optimal network
solution for distant clocks as well as for clocks positioned in close proximity
of each other. In the second scenario, we employ collective dissipation to
drive two clocks with oppositely oriented Bloch vectors into a steady state
entanglement. The corresponding EPR entanglement provides enhanced time sharing
beyond the projection noise limit between the two quantum synchronized clocks
protected from eavesdropping, as well as allows better characterization of
systematic effects.
