Local entanglement transfer to multiple pairs of spatially separated observers

TL;DR

This paper explores how to transfer entanglement from a single entangled pair to multiple pairs of spatially separated observers using local unitaries, enabling efficient sharing of quantum resources.

Contribution

It introduces a method to sequentially transfer entanglement to multiple pairs with limited initial entanglement, optimizing the process with local unitaries.

Findings

Entanglement can be transferred to multiple pairs using joint unitaries.

The maximum number of pairs receiving entanglement depends on initial entanglement.

Optimal local unitaries maximize the number of pairs with at least a fixed entanglement amount.

Abstract

Entanglement is an advantageous but at the same time a costly resource utilized in various quantum tasks. For an efficient usage and deployment of entanglement, we envisage the scenario where a pair of spatially separated observers, Charu and Debu, want to share entanglement without interacting with each other. As a way out, their systems can separately and locally interact with those of Alice and Bob, respectively, who already share an entangled state. We ask if it is possible to transfer entanglement from the Alice-Bob pair to multiple Charu- Debu pairs, where the Alice-Bob pair only possesses a limited amount of pre-shared entanglement. We find joint unitaries, which when applied by Alice and one of the Charus, and by Bob and the corresponding Debu, such that a nonzero amount of the entanglement shared between Alice and Bob can be sequentially transferred to an indefinite number of pairs of Charus and Debus. We discuss the amount of entanglement that can be transferred to a fixed number of pairs using these unitaries. Also, we determine to how many pairs a fixed amount of entanglement can be transferred. Moreover, by optimizing over all possible local unitaries, we analyze the maximum number of pairs to which entanglement can be transferred in such a way that each pair gets at least a fixed amount of entanglement.