Detecting some three-qubit MUB diagonal entangled states via nonlinear optimal entanglement witnesses |
| |
Authors: | M A Jafarizadeh M Mahdian A Heshmati K Aghayar |
| |
Institution: | (1) Department of Theoretical Physics and Astrophysics, University of Tabriz, Tabriz, 51664, Iran;(2) Institute for Studies in Theoretical Physics and Mathematics, Tehran, 19395-1795, Iran;(3) Research Institute for Fundamental Sciences, Tabriz, 51664, Iran |
| |
Abstract: | The three qubits mutually unbiased bases (MUB) diagonal density matrices with maximally entanglement in Greenberger-Horne-Zeilinger
(GHZ) basis are studied. These are a natural generalization of Bell-state diagonal density matrices. The linearity of positive
partial transpose (PPT) conditions allows one to specify completely PPT states or feasible region (FR) which form a polygon,
where the projection of the feasible region to some two dimensional planes has lead to better visualization. To reveal the
PPT entangled regions of these density matrices, we manipulate some appropriate optimal non-decomposable linear entanglement
witnesses (EWs) as the envelope of family of linear optimal non-decomposable EWs. These nonlinear EWs are nonlinear functional
of MUB diagonal states, so that they are nonnegative valued over all separable, but they are negative valued over some PPT
entangled MUB diagonal states. Even though, these nonlinear EWs can not separate completely, the PPT entanglement region from
separable one, but however in special cases they lead to necessary and sufficient condition for separability. To support the
evidence, we study three categories for special choices of parameters in density matrices, and using the nonlinear EWs we
can distinguish the region of PPT entangled states and separable states, completely. At the end some numerical simulations
are provided to show the practical applicability of these nonlinear EWs in detecting some PPT entangled MUB diagonal states. |
| |
Keywords: | PACS" target="_blank">PACS 03 67 Mn Entanglement measures witnesses and other characterizations 03 65 Ud Entanglement and quantum nonlocality (e g EPR paradox Bell’ s inequalities GHZ states etc ) |
本文献已被 SpringerLink 等数据库收录! |
|