Relation between the Greenberger-Horne-Zeilinger--entanglement cost of preparing a multipartite pure state and its quantum discord

TL;DR

This paper establishes a relationship between the GHZ entanglement cost of preparing multipartite pure states and their quantum discord, providing an operational interpretation of discord in quantum state preparation.

Contribution

It introduces a LOCC protocol that asymptotically converts GHZ states into any multipartite pure state with a rate equal to the state's multipartite discord.

Findings

GHZ-entanglement cost is bounded by multipartite discord

Operational interpretation of multipartite discord for pure states

Protocol asymptotically converts GHZ states to target states

Abstract

We investigate how much amount of Greenberger-Horne-Zeilinger (GHZ) entanglement is required in order to prepare a given multipartite state by local operations and classical communication (LOCC).We present a LOCC procedure that asymptotically converts GHZ states into an arbitrary multipartite pure state, whose conversion rate is given by the multipartite discord of the state. This reveals that the GHZ-entanglement cost of preparing a pure state is not higher than the multipartite discord of the state. It also provides an operational interpretation of multipartite discord for pure states, namely, the consumption rate of GHZ entanglement in the devised procedure.