Abstract
Using the convex semidefinite programming method and superoperator formalism we obtain the finite quantum tomography of some mixed quantum states such as: truncated coherent states tomography, phase tomography and coherent spin state tomography, qudit tomography, N-qubit tomography, where that obtained results are in agreement with those of References (Buzek et al., Chaos, Solitons and Fractals 10 (1999) 981; Schack and Caves, Separable states of N quantum bits. In: Proceedings of the X. International Symposium on Theoretical Electrical Engineering, 73. W. Mathis and T. Schindler, eds. Otto-von-Guericke University of Magdeburg, Germany (1999); Pegg and Barnett Physical Review A 39 (1989) 1665; Barnett and Pegg Journal of Modern Optics 36 (1989) 7; St. Weigert Acta Physica Slov. 4 (1999) 613).
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Barnett, S. M. and Pegg, D. T. (1989). Journal of Modern Optics 36, 7.
Barnum, H., Saks, M., and Szegedy, M. (2003). In Proceedings of the 18th IEEE Annual Conference on Computational Complexity, p. 179.
Boyd, S., El Ghaoui, L., Feron, E., and Balakrishnan, V. (1994). Linear matrix in-equalities in system and control theory. Society for Industrial and Applied Mathematics.
Buzek, V. R. and Drobny, G. (2000). Journal of Modern Optics 47, 2823.
Buzek, V., Drobny, G., Derka, R., Adam, G., and Wiedeman, H. (1999). Chaos, Solitons and Fractals 10, 981.
Casazza, P. G., Fickus, M., Kovacevic, J., Leona, M. T., and Tremain, J. C. (2003). A Physical Interpretation for Finite Tight Frames, preprint.
Christensen, O. and Jensen, T. K. (1999). An Introduction to the Theory of Bases, Frames and Wavelets. Technical University of Denmark, Lecture Note.
D'Ariano, G. M. (1990). Advances in Physics 39, 191.
D'Ariano, G. M., Mancini, S., Manko, V. I., and Tombesi, P. (1996). Journal of Optics B: Quantum and Semiclassical Optics 8, 1017.
D'Ariano, G. M., Maccone, L., and Paris, M. G. A. (2001). Journal of Physics A (Mathematical and General) 34, 93.
Davidson, T. N., Luo, Z.-Q., and Wong, K. M. (2000). Design of orthogonal pulse shapes for communications via semidefinite programming. IEEE Transactions on Signal Processing 48, 1433.
Doherty, A. C., Parrilo, P. A., and Spedalieri, F. M. (2002). Physical Review Letters 88, 187904.
Eldar, Y. C., Megretski, A., and Verghese, G. C. (2003). IEEE Transactions on Information Theory 49, 1007.
Glauber, R. J. (1963a). Physical Review 130, 2529. ibid. 131, 2766 (1963).
Glauber, R. J. (1963b). Physical Review 131, 2766.
Goemans, M. X. and Williamson, D. P. (1995). Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming. Journal of the Association for Computing Machinery 42, 1115.
Helstrom, C. W. (1976). Quantum Detection and Estimation Theory. Academic Press.
Kim, H. O. and Lim, J. K. (1997). Applied and Computional Harmonic Analysis 4, 222.
Kitaev, A. (2002). Quantum coin flipping. Talk at Quantum Information Processing 2003, slides and video at http://www.msri.org, December.
Kuang, L. M., Wang, F. B., and Zhou, Y. G. (1993). Physics Letters A 183(1).
Kuang, L. M., Wang, F. B., and Zhou, Y. G. (1994). Journal of Modern Optics 41, 1307.
Lawrence. (2003). Ip, Shor's Algorithm is Optimal, University of California, Berkeley, USA MU Seminar, http://www.qcaustralia.org.
Luo, Z. Q. (2003). Applications of convex optimization in signal processing and digital communication. Mathematical Programming Series B 97, 177.
Ma, W. K., Davidson, T. N., Wong, K. M., Luo, Z.-Q., and Ching, P. C. (2002). Quasi-maximum-likelihood multiuser detection using semidefinite relaxation with application to synchronous CDMA. IEEE Transactions on Signal Processing 50, 912.
McAlister, D. F. and Raymer, M. G. (1997). Physical Review A 55, R1609.
Miquel, C., Paz, J. P., and Saraceno, M. (2002). Physics Review A 65.
Miranowicz, M., Leonski, W., and Imoto (2001). Advances in Chemical Physics 119(Part 1). Nonlinear optics.
Miranowicz, A., Piatek, K., and Tanas, R. (1994). Physical Review A 50, 3423.
Parrilo, P. A., Doherty, A. C., and Spedalieri, F. M. (2002). Proceedings of the 41st IEEE Conference of Decision and Control.
Pegg, D. T. and Barnett, S. M. (1989). Physical Review A 39, 1665.
Rains, E. M. (2001). IEEE Transactions on Information Theory 47, 2921.
Raymer, M. G. and Schleich, W. (1997). Special issue on quantum state preparation and measurement. Journal of Modern Optics 44, 11.
Rungta, P., Munro, W. J., Nemoto, K., Deuar, P., Milburn, G. J., and Caves, C. M. quant-ph/0001075.
Schack, R. and Caves, C. M. (1999). Separable states of N quantum bits. In: Proceedings of the X. International Symposium on Theoretical Electrical Engineering, 73. In W. Mathis and T. Schindler, eds. Otto-von-Guericke University of Magdeburg, Germany.
St. Weigert (1999). Acta Physica Slov. 4, 613.
Vandenberghe, L. and Boyd, S. (1996). SIAM Review 38, 49.
Vandenberghe, L. and Boyd, S. (unpublished). http://www.stanford.edu/boyd/cvxbook.html.
Author information
Authors and Affiliations
Corresponding author
Additional information
PACs index: 03.65.Ud
Rights and permissions
About this article
Cite this article
Mirzaee, M., Rezaee, M. & Jafarizadeh, M.A. Finite Quantum Tomography and Semidefinite Programming. Int J Theor Phys 46, 1471–1494 (2007). https://doi.org/10.1007/s10773-006-9287-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10773-006-9287-9