Artículos de revistas
Global Convergence Of Diluted Iterations In Maximum-likelihood Quantum Tomography
Registro en:
Quantum Information And Computation. Rinton Press Inc., v. 14, n. 11/12/15, p. 966 - 980, 2014.
15337146
2-s2.0-84904422367
Autor
Goncalves D.S.
Gomes-Ruggiero M.A.
Lavor C.
Institución
Resumen
In this paper we address convergence issues of the Diluted RpR algorithm [1], used to obtain the maximum likelihood estimate for the density matrix in quantum state tomography. We give a new interpretation to the diluted RpR iterations that allows us to prove the global convergence under weaker assumptions. Thus, we propose a new algorithm which is globally convergent and suitable for practical implementation. © Rinton Press. 14 11/12/15 966 980 Řeháček, J., Hradil, Z., Knill, E., Lvovsky, A.I., Diluted maximum-likelihood algorithm for quantum tomography (2007) Phys. Rev. A, 75, p. 042108 Hradil, Z., Quantum-state estimation (1997) Phys. Rev. A, 55, pp. R1561-R1564 Paris, M., Rehácek, J., Quantum State Estimation, Lecture Notes in Physics (2004), 649. , Springer, editorsGonçalves, D.S., Lavor, C., Gomes-Ruggiero, M.A., Cesário, A.T., Vianna, R.O., Maciel, T.O., Quantum state tomography with incomplete data: Maximum entropy and variational quantum tomography (2013) Phys. Rev. A, 87, p. 052140 Kowada, L., Lavor, C., Portugal, R., Figueiredo, C., A new quantum algorithm for solving the minimum searching problem (2008) International Journal of Quantum Information, 6, pp. 427-436 Nielsen, M., Chuang, I., (2004) Quantum Computation and Quantum Information, , Cambridge Series on Information and the Natural Sciences, 1st edition, Cambridge University Press Alves, R., Lavor, C., Clifford algebra applied to Grover's algorithm (2010) Advances in Applied Clifford Algebra, 20, pp. 447-488 Evangelista, T., Lavor, C., Rabelo, W.R.M., A new method to calculate the inconclusive coefficients in the quantum state discrimination (2011) International Journal of Modern Physics C, 22, pp. 95-105 Melo, N., Lavor, C., A Clifford Algebra of Signature (n, 3n) and the Density Operators of Quantum Information Theory (2013) Advances in Applied Clifford Algebras, 23, pp. 143-152 Maciel, T.O., Vianna, R.O., Optimal estimation of quantum processes using incomplete information: Variational quantum process tomography (2012) Quantum Information and Computation, 12, pp. 0442-0447 Hradil, Z., Řeháček, J., Fiurášek, J., Ježek, M., Maximum-Likelihood Methods in Quantum Mechanics, in Quantum State Estimation, Lecture Notes in Physics (2004), 649, pp. 163-172. , SpringerJames, D.F.V., Kwiat, P.G., Munro, W.J., White, A.G., Measurement of qubits (2001) Phys. Rev. A, 64, p. 052312 Wolf, P., Convergence Conditions for Ascent Methods (1969) SIAM Review, 11, pp. 226-235 Wolf, P., Convergence Conditions for Ascent Methods. II: Some Corrections (1971) SIAM Review, 13, pp. 185-188 Nocedal, J., Wright, S.J., (1999) Numerical Optimization, , Springer Armijo, L., Minimization of functions having Lipschitz continuous first partial derivatives (1966) Pacific Journal of Mathematics, 16, pp. 1-3 Bertsekas, D.P., (1999) Nonlinear programming, , Athena Scientific de Klerk, E., (2002) Aspects of Semidefinite Programming: Interior Point Algorithms and Selected Applications, , Kluwer Academic Publishers Toh, K.C., Todd, M.J., Tutuncu, R.H., SDPT3-a Matlab software package for semidefinite programming (1999) Optimization Methods and Software, 11, pp. 545-581 Borchers, B., A C Library for Semidefinite Programming (1999) Optimization Methods and Soft-ware, 11, pp. 613-623 Gonçalves, D.S., Gomes-Ruggiero, M.A., Lavor, C., Farías, O.J., Ribeiro, P.H.S., Local solutions of Maximum Likelihood Estimation in Quantum State Tomography (2012) Quantum Informa-tion and Computation, 12, pp. 775-790 Vardi, Y., Lee, D., From Image Deblurring to Optimal Investments: Maximum Likelihood Solutions for Positive Linear Inverse Problems (1993) Journal of the Royal Statistical Society, Series B (Methodological), 55, pp. 569-612