Entanglement-swapping boxes and their communication properties

We pose the fundamental question of communication properties of primitives irrespectively of their implementation. To illustrate the idea we introduce the concept of entanglement-swapping boxes, i.e., we consider any quantum operations which perform entanglement swapping, not necessarily via simple quantum teleportation. We ask a question about the properties of such boxes, i.e., what local operations and how much classical communication are needed to perform them. We also ask if any box which performs entanglement swapping can be used to establish classical communication. We show that each box needs at least two bits of classical communication to perform it. It is also shown that each box can be used for classical communication and, most importantly, that there exist boxes which allow one to communicate at most one bit. Surprisingly we find basic irreversibility in the process of entanglement swapping with respect to its classical communication properties.

Figure 1

Entanglement swapping (continuous arrow) in two steps (dashed arrows): from two EPR pairs to a GHZ state, to the final EPR pair. Lines denote quantum correlations.

Figure 2

Entanglement swapping (black) box. (a) Defining action of an ES box. Time goes from left to right. (b) Actual (LOCC) implementation of a given ES box.