Entanglement witnesses and semidefinite programming

Proceedings of the IEEE Conference on Decision and Control

Volumn 4, Issue , 2002, Pages 4575-4580

  Parrilo, Pablo A ^a   Doherty, Andrew C ^b   Spedalieri, Federico M ^b  

^a ETH ZURICH   (Switzerland)

^b CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

LINEAR CONTROL SYSTEMS; MATRIX ALGEBRA; PROBABILITY DISTRIBUTIONS; QUANTUM THEORY; TENSORS;

ENTANGLEMENT WITNESSES; POSITIVE PARTIAL TRANSPOSE; SEMIDEFINITE PROGRAMMING;

OPTIMIZATION;

EID: 0036991369     PISSN: 01912216     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (18)

1. J. S. Bell, On the Einstein-Podolsky-Rosen paradox. Physics, 1:195-200, 1964.
2. S. L. Braunstein, C. M. Caves, R. Jozsa, N. Linden, S. Popescu, and R. Schack. Separability of very noisy mixed states and implications for NMR quantum computing. Phys. Rev. Lett., 83(5):1054-1057, 1999.
3. D. Bruss and A. Peres. Construction of quantum states with bound entanglement. Phys. Rev. A, 61:030301(R), 2000.
4. A. C. Doherty, P. A. Parrilo, and F. M. Spedalieri. Distinguishing separable and entangled states. Phys. Rev. Lett., 88(18):187904-1-4, May 2002.
5. M. Horodecki, P. Horodecki, and R. Horodecki. Separability of mixed states: necessary and sufficient conditions. Phys. Lett. A, 223:1, 1996.
6. M. Horodecki, P. Horodecki, and R. Horodecki. Mixed-state entanglement and quantum communication. quant-ph/0109124, 2001.
7. P. Horodecki. Separability criterion and inseparable mixed states with positive partial transpose. Phys. Lett. A, 232:233, 1997.
8. M. Lewenstein, D. Bruss, J. I. Cirac, B. Kraus, M. Kraus, J. Samsonowicz, A. Sanpera, and R. Tarrach. Separability and distillability in composite quantum systems -a primer-. J. Mod. Opt., 47:2841, 2000.
9. M. Lewenstein, B. Kraus, J. I. Cirac, and P. Horodecki. Optimization of entanglement witnesses. Phys. Rev. A, 62:052310, 2000.
10. M. N. Nielsen, and I. L. Chuang. Quantum computation and quantum information. Cambridge University Press, Cambridge, 2000.
11. P. A. Parrilo. Structured Semidefinite Programs and Semialgebraic Geometry Methods in Robustness and Optimization. PhD thesis, California Institute of Technology, May 2000. Available at http://www.cds.caltech.edu/~pablo/.
12. P. A. Parrilo. Semidefinite programming relaxations for semialgebraic problems. To appear in Mathematical Programming, available at http://www.control.ethz.ch/~parrilo/pubs/2001.
13. A. Peres. Separability criterion for density matrices. Phys. Rev. Lett., 77(8):1413-1415, 1996.
14. B. Reznick, Some concrete aspects of Hilbert's 17th problem. In Contemporary Mathematics, volume 253, pages 251-272. American Mathematical Society, 2000.
15. J. F. Sturm. Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones. Optimization Methods and Software, 11-12:625-653, 1999. Available at http://fewcal.kub.nl/sturm/software/sedumi.html.
16. B. M. Terhal. Bell inequalities and the separability criterion. Phys. Lett. A, 271(5-6):319-326, 2000.
17. L. Vandenberghe and S. Boyd. Semidefinite programming. SIAM Review, 38 (1):49-95, 1996.
18. R. F. Werner. Quantum states with Einstein-Podolsky-Rosen correlations admitting a hidden-variable model. Phys. Rev. A, 40(8):4277-4281, 1989.