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We investigate entanglement between collective operators of two blocks ofoscillators in an infinite linear harmonic chain. These operators are definedas averages over local operators (individual oscillators) in the blocks. On theone hand, this approach of "physical blocks" meets realistic experimentalconditions, where measurement apparatuses do not interact with singleoscillators but rather with a whole bunch of them, i.e., where in contrast tousually studied "mathematical blocks" not every possible measurement isallowed. On the other, this formalism naturally allows the generalization toblocks which may consist of several non-contiguous regions. We quantifyentanglement between the collective operators by a measure based on thePeres-Horodecki criterion and show how it can be extracted and transferred totwo qubits. Entanglement between two blocks is found even in the case wherenone of the oscillators from one block is entangled with an oscillator from theother, showing genuine bipartite entanglement between collective operators.Allowing the blocks to consist of a periodic sequence of subblocks, we verifythat entanglement scales at most with the total boundary region. We also applythe approach of collective operators to scalar quantum field theory.Comment: 7 pages, 4 figures, significantly revised version with new results,  journal reference adde

Entanglement between collective operators in a linear harmonic chain