Entanglement sharing with separable states

TL;DR

This paper introduces a protocol for sharing entanglement using only separable Gaussian states, revealing new ways to generate and manipulate entanglement without transmitting entangled states directly.

Contribution

It presents a novel entanglement sharing protocol based on separable states and demonstrates how entanglement can be mediated without transmitting entangled modes.

Findings

Entanglement can be created via separable states and local operations.

The protocol shows nontrivial signatures of bound entanglement.

Switching between different separability classes is possible with coherent operations.

Abstract

We propose an entanglement sharing protocol based on separable states. Initially, two parties, Alice and Bob, share a two-mode separable Gaussian state. Alice then splits her mode into two separable modes and distributes them between two players. Bob is separable from the players but he can create entanglement with either of the players if the other player moves to his location and collaborates with him. Any two parties are separable and the creation of entanglement is thus mediated by transmission of a mode which is separable from individual modes on Alice's and Bob's side. For the state shared by the players and Bob one cannot establish entanglement between any two modes even with the help of operation on the third mode provided that Bob is restricted to Gaussian measurements and the state thus carries a nontrivial signature of bound entanglement. The present protocol also demonstrates switching between different separability classes of tripartite systems by coherent operations on its bipartite parts and complements studies on protocols utilizing mixed partially entangled multipartite states.