Distribution of continuous-variable entanglement by separable Gaussian states

Abstract

Entangling two systems at distant locations using a separable mediating ancilla is a counterintuitive phenomenon proposed for qubits by T. Cubitt et al. ͓Phys. Rev. Lett. 91, 037902 ͑2003͔͒. We show that such entanglement distribution is possible with Gaussian states, using a certain three-mode fully separable mixed Gaussian state and linear optics elements readily available in experiments. Two modes of the state become entangled by sequentially mixing them on two beam splitters, while the third one remains separable in all stages of the protocol.

Systematics of entanglement distribution by separable states

“…To remove the entanglement of the two ancillas D 1 and D 2 from the rest of states we again use the procedure of mixing and symmetrization. We first mix the final state (14) and form ρ…”

“…Several questions remain for future investigations: First one can consider other classes of multi-partite states, like W states, 1-uniform states [28] and cluster states [29] which are important for one-way quantum computation. Second one may see how GHZ state sharing with separable states can be implemented with Gaussian variables along the the theoretical lines set in [14,15] and their experimental realization in [16][17][18]. Finally, investigation of the cost of multi-partite entanglement sharing [22], [23] and its relation with multi-partite quantum correlation present in the initial states, will surf again, a study which may lead to a host of connections and bounds between two not-well understood concepts.…”

Excessive distribution of quantum entanglement

“…[5] and further examples were presented in Refs. [6][7][8][9]. However, to the best of our knowledge, an analytical example of excessive protocol with non-zero communicated entanglement will be presented here for the first time.…”

“…This finding has attracted considerable attention, resulting in several theoretical proposals [6][7][8][9] and inspiring test-bed experimental realizations [10][11][12][13]. On the other hand, it generated great curiosity on what really limits the distribution, if not the carried entanglement.…”

“…In indirect schemes, one starts with the subsystems already apart and uses ancillary systems as communication channels between the laboratories to establish entanglement between them. This class encompasses, among others, the intriguing protocols that rely only on separable ancillary carriers mentioned above [5][6][7][8][9][10][11][12][13]. They reveal that, even if no entanglement is being communicated, i.e.…”