Abstract. We study the closest disentangled state to a given entangled state in any system (multi-party with any dimension). We obtain the set of equations the closest disentangled state must satisfy, and show that its reduction is strongly related to the extremal condition of the local filtering on each party. Although the equations we obtain are not still tractable, we find some sufficient conditions for which the closest disentangled state has the same reduction as the given entangled state. Further, we suggest a prescription to obtain a tight upper bound of the relative entropy of entanglement in two-qubit systems.

PACS numbers: 03.67.−a, 03.65.Ud

Print publication: Issue 38 (27 September 2002)
Received 19 April 2002, in final form 16 July 2002
Published 12 September 2002