title: Irreversibility for all bound entangled states.
abstract: We derive a new inequality for entanglement for a mixed four-partite state. Employing this inequality, we present a one-shot lower bound for entanglement cost and prove that entanglement cost is strictly larger than zero for any entangled state. We demonstrate that irreversibility occurs in the process of formation for all nondistillable entangled states. In this way we solve a long standing problem of how "real" is entanglement of bound entangled states. Using the new inequality we also prove the impossibility of local cloning of a known entangled state.
authors.affiliation: Institute of Theoretical Physics and Astrophysics, University of Gdańsk, 80-952 Gdańsk, Poland. dyang@ustc.edu.cn
authors.forename: Dong
authors.initials: D
authors.lastname: Yang
authors.forename: Michał
authors.initials: M
authors.lastname: Horodecki
authors.forename: Ryszard
authors.initials: R
authors.lastname: Horodecki
authors.forename: Barbara
authors.initials: B
authors.lastname: Synak-Radtke