Mixed-state sensitivity of several quantum-information benchmarks

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 70, Issue 5 A, 2004, Pages

  Peters, Nicholas A ^a   Wei, Tzu Chieh ^a   Kwiat, Paul G ^a  

^a United States of America   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BENCHMARKING; EIGENVALUES AND EIGENFUNCTIONS; ENTROPY; MATHEMATICAL MODELS; MATHEMATICAL OPERATORS; MICROELECTROMECHANICAL DEVICES; PERTURBATION TECHNIQUES; PHOTONS; POLARIZATION;

LINEAR ENTROPY; POLARIZED PHOTONS; QUANTUM CLONING; VON NEUMANN ENTROPY; WERNER STATES;

QUANTUM THEORY;

EID: 37649030607     PISSN: 10502947     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevA.70.052309     Document Type: Article

References (23)

1. R. Jozsa, J. Mod. Opt. 41, 2315 (1994).
2. C. H. Bennett et al., Phys. Rev. Lett. 76, 722 (1996).
3. A. Kent, Phys. Rev. Lett. 81, 2839 (1998).
4. F. Verstraete and H. Verschelde, Phys. Rev. Lett. 90, 097901 (2003).
5. N. Gisin and S. Massar, Phys. Rev. Lett. 79, 2153 (1997).
6. S. Ishizaka and T. Hiroshima, Phys. Rev. A 62, 022310 (2001).
7. F. Verstraete, K. Audenaert, and B. DeMoor, Phys. Rev. A 64, 012316 (2001).
8. W. J. Munro, D. F. V. James, A. G. White, and P. G. Kwiat, Phys. Rev. A 64, 030302(R) (2001).
9. W. K. Wootters, Phys. Rev. Lett. 80, 2245 (1998).
10. V. Coffman, J. Kundu, and W. K. Wootters, Phys. Rev. A 61, 052306 (2000).
11. S. Bose and V. Vedral, Phys. Rev. A 61, 040101(R) (2000).
12. N. A. Peters et al., Phys. Rev. Lett. 92, 133601 (2004).
13. R. F. Werner, Phys. Rev. A 40, 4277 (1989).
14. Note that for certain entanglement and mixedness parameter-izations, the Werner states are the MEMS [T. C. Wei et al., Phys. Rev. A 67, 022110 (2003)].
15. Y. S. Zhang, Y. F. Huang, C. F. Li, and G. C. Guo, Phys. Rev. A 66, 062315 (2002).
16. M. Barbieri, F. DeMartini, G. DiNepi, and P. Mataloni, Phys. Rev. Lett. 92, 177901 (2004).
17. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, U.K., 2000).
18. N. A. Peters, T.-C. Wei, and P. G. Kwiat, Proc. SPIE 5468, 269 (2004).
19. F. Verstraete and H. Verschelde, Phys. Rev. A 66, 022307 (2002).
20. M. Horodecki, P. Horodecki, and R. Horodecki, Phys. Rev. Lett. 78, 574 (1997).
21. In more detail, we project the ideal target state into 16 basis vectors, such as 〈00|, |〈11|, 〈(0+i1)0|, etc., to obtain a list of probabilities of given "measurement" outcomes. These probabilities are then multiplied by a constant number simulating an expected average number of counts in a total basis measure ment, e.g., what one would expect to observe when projecting into 〈00|, 〈|01|, 〈10|, and 〈11|. Next, each of these ideal counts (plus 1 to avoid zero distributions) is used as the mean of a Poisson distribution, from which a random number is generated. These "measurement" values are then processed using a maximum likelihood technique to give a physically valid perturbed density matrix [D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, Phys. Rev. A 64, 052312 (2001); J. B. Altepeter, D. F. V. James, and P. G. Kwiat, Quantum State Estimation, edited by M. Paris and J. Rehacek (Springer, Berlin, 2004), Chap. 3]. If the fidelity between the perturbed density matrix and the target state is greater than 0.9900, the tangle and linear entropy are calculated and plotted in Fig. 2.
22. N. Peters et al., Quantum Inf. Comput. 3, 503 (2003).
23. E. Knill, R. Laflamme, and W. H. Zurek, Science 279, 574 (1998).