Greenberger-Horne-Zeilinger Entanglement Cost Of Preparing A Multipartite Pure State Is Not Higher Than Quantum Discord

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 a previously unknown fact 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.

pacs:
03.67.-a, 03.67.Bg, 03.67.Mn, 03.67.Ac

Introduction.- Quantum entanglement lies at the heart of notable features of quantum physics and the power of quantum information processing Jozsa03 ; Bennet92 ; Bennet93 ; Giovannetti04 . Its quantification is an issue of great importance. A possible approach is based on the idea that entanglement is a resource shared between distant parties that cannot be generated by local operations and classical communication (LOCC). More specifically, a scale of entanglement can be created by considering asymptotic conversion (i.e., conversion of m