  We investigate entanglement between collective operators of two blocks of
oscillators in an infinite linear harmonic chain. These operators are defined
as averages over local operators (individual oscillators) in the blocks. On the
one hand, this approach of "physical blocks" meets realistic experimental
conditions, where measurement apparatuses do not interact with single
oscillators but rather with a whole bunch of them, i.e., where in contrast to
usually studied "mathematical blocks" not every possible measurement is
allowed. On the other, this formalism naturally allows the generalization to
blocks which may consist of several non-contiguous regions. We quantify
entanglement between the collective operators by a measure based on the
Peres-Horodecki criterion and show how it can be extracted and transferred to
two qubits. Entanglement between two blocks is found even in the case where
none of the oscillators from one block is entangled with an oscillator from the
other, showing genuine bipartite entanglement between collective operators.
Allowing the blocks to consist of a periodic sequence of subblocks, we verify
that entanglement scales at most with the total boundary region. We also apply
the approach of collective operators to scalar quantum field theory.
