Abstract
We investigate the issue of finding common entanglement witness for certain class of states and extend this study to the case of Schmidt number witnesses. We also introduce the notion of common decomposable and non-decomposable witness operators which is specially useful for constructing a common witness where one of the entangled states is with a positive partial transpose. Our approach is illustrated with the help of suitable examples of qutrit systems.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bennett C.H., Brassard G., Crepeau C., Jozsa R., Peres A., Wootters W.K.: Teleporting an unknown quantum state via dual classical and Einstein–Podolsky–Rosen channels. Phys. Rev. Lett. 70, 1895 (1993)
Bennett C.H., Wiesner S.J.: Communication via one- and two-particle operators on Einstein– Podolsky–Rosen states. Phys. Rev. Lett. 69, 2881 (1992)
Bennett, C.H., Brassard, G.: Quantum cryptography: public key distribution and coin tossing. In: Proceeding of IEEE International Conference on Comp., Sys., and Sig. Proc., p. 175. Bangalore, India, (1984)
Barenco A., Deutsch D., Ekert A., Jozsa R.: Conditional quantum dynamics and logic gates. Phys. Rev. Lett. 74, 4083 (1995)
Peres A.: Separability criterion for density matrices. Phys. Rev. Lett. 77, 1413 (1996)
Horodecki M., Horodecki P., Horodecki R.: Separability of mixed states: necessary and sufficient conditions. Phys. Lett. A 223, 1 (1996)
Terhal B.M.: Bell inequalities and the separability criterion. Phys. Lett. A 271, 319 (2000)
Lewenstein M., Krauss B., Cirac J.I., Horodecki P.: Optimization of entanglement witnesses. Phys. Rev. A 62, 052310 (2000)
Doherty A.C., Parrilo P.A., Spedalieri F.M.: Complete family of separability criteria. Phys. Rev. A 69, 022308 (2004)
Sperling J., Vogel W.: Necessary and sufficient conditions for bipartite entanglement. Phys. Rev. A 79, 022318 (2009)
Sanpera A., Bruβ D., Lewenstein M.: Schmidt-number witnesses and bound entanglement. Phys. Rev. A 63, 050301(R) (2001)
Terhal B.M., Horodecki P.: Schmidt number for density matrices. Phys. Rev. A 61, 040301(R) (2000)
Sperling J., Vogel W.: Determination of the Schmidt number. Phys. Rev. A 83, 042315 (2011)
Wu Y.C., Guo G.C.: Determining the existence of the common entanglement witnesses for some entangled states. Phys. Rev. A 75, 052333 (2007)
Ganguly N., Adhikari S.: Witness for edge states and its characteristics. Phys. Rev. A 80, 032331 (2009)
Augusiak R., Grabowski J., Kus M., Lewenstein M.: Searching for extremal PPT entangled states. Opt. Commun. 283, 805 (2010)
Acin A., Bruβ D., Lewenstein M., Sanpera A.: Classification of mixed three-qubit states. Phys. Rev. Lett. 87, 040401 (2001)
Horodecki P., Horodecki M., Horodecki R.: Bound entanglement can be activated. Phys. Rev. Lett. 82, 1056 (1999)
Terhal B.M.: A family of indecomposable positive linear maps based on entangled quantum states. Linear Algebra Its Appl. 323, 61 (2001)
Hyllus P., Moura Alves C., Bruβ D., Macchiavello C.: Generation and detection of bound entan-glement. Phys. Rev. A 70, 032316 (2004)
Guhne O., Hyllus P., Bruβ D., Ekert A., Lewenstein M., Macchiavello C., Sanpera A.: Experimental detection of entanglement via witness operators and local measurements. J. Mod. Opt. 50, 1079 (2003)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Ganguly, N., Adhikari, S. & Majumdar, A.S. Common entanglement witnesses and their characteristics. Quantum Inf Process 12, 425–436 (2013). https://doi.org/10.1007/s11128-012-0386-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11128-012-0386-7