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2015

Practical, Reliable Error Bars in Quantum Tomography

Faist, Philippe, Renner, Renato

Understand

Precise characterization of quantum devices is usually achieved with quantum tomography.

However, most methods which are currently widely used in experiments, such as maximum likelihood estimation, lack a well-justified error analysis.
Promising recent methods based on confidence regions are difficult to apply in practice or yield error bars which are unnecessarily large.
Here, we propose a practical yet robust method for obtaining error bars.

Built on

N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller, The Journal of Chemical Physics 21
1953
Earlier work this paper cites.
C. W. Helstrom, Journal of Statistical Physics 1
1969
Earlier work this paper cites.
K. Vogel and H. Risken, Physical Review A 40
1989
Earlier work this paper cites.
B. Efron and R. J. Tibshirani, An Introduction to the Bootstrap (CRC Press, 1994) p. 456
1994
Earlier work this paper cites.
Z. Hradil, Physical Review A 55
1997
Earlier work this paper cites.
I. L. Chuang and M. A. Nielsen, Journal of Modern Optics 44
1997
Earlier work this paper cites.
C. H. Bennett and D. P. DiVincenzo, Nature 404
2000
Earlier work this paper cites.
G. M. D’Ariano, Physics Letters A 268
2000
Earlier work this paper cites.
G. Cassinelli, G. M. D’Ariano, E. De Vito, and A. Levrero, Journal of Mathematical Physics 41
2000
Earlier work this paper cites.
J. Řeháček, Z. Hradil, and M. Ježek, Physical Review A 63
2001
Earlier work this paper cites.
D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, Physical Review A 64
2001
Earlier work this paper cites.
K. Zyczkowski and H.-J. Sommers, Journal of Physics A 34
2001
Earlier work this paper cites.
A. Alexandrescu, Modern C++ Design: Generic Programming and Design Patterns Applied (Addison-Wesley Professional, 2001) p. 323
2001
Earlier work this paper cites.
R. T. Thew, A. G. White, and W. J. Munro, Physical Review A 66
2002
Earlier work this paper cites.
G. M. D’Ariano, M. G. A. Paris, and M. F. Sacchi, Advances in Imaging and Electron Physics 128
2003
Earlier work this paper cites.
M. W. Mitchell, C. W. Ellenor, S. Schneider, and A. M. Steinberg, Physical Review Letters 91
2003
Earlier work this paper cites.
G. Kimura, Physics Letters A 314
2003
Earlier work this paper cites.
M. S. Byrd and N. Khaneja, Physical Review A 68
2003
Earlier work this paper cites.
M. Paris and J. Řeháček, eds., Quantum State Estimation , Lecture Notes in Physics, Vol. 649 (Springer, Berlin, Heidelberg, 2004)
2004
Earlier work this paper cites.
A. I. Lvovsky, Journal of Optics B: Quantum and Semiclassical Optics 6
2004
Earlier work this paper cites.
J. L. O’Brien, G. J. Pryde, A. Gilchrist, D. F. V. James, N. K. Langford, T. C. Ralph, and a. G. White, Physical Review Letters 93
2004
Earlier work this paper cites.
R. Blume-Kohout and P. Hayden, ArXiv e-prints (2006), arXiv:quant-ph/0603116 [quant-ph]
2006
Earlier work this paper cites.
I. Bengtsson and K. Zyczkowski, Geometry of Quantum States: An Introduction to Quantum Entanglement (Cambridge University Press, Cambridge, UK, 2006)
2006
Earlier work this paper cites.
J. Řeháček, Z. Hradil, E. Knill, and A. Lvovsky, Physical Review A 75
2007
Earlier work this paper cites.
A. F. Albuquerque, F. Alet, P. Corboz, P. Dayal, A. Feiguin, S. Fuchs, L. Gamper, E. Gull, S. Gürtler, A. Honecker, R. Igarashi, M. Körner, A. Kozhevnikov, A. Läuchli, S. R. Manmana, M. Matsumoto, I. P. McCulloch, F. Michel, R. M. Noack, G. Pawłowski, L. Pollet, T. Pruschke, U. Schollwöck, S. Todo, S. Trebst, M. Troyer, P. Werner, and S. Wessel, Journal of Magnetism and Magnetic Materials 310
Original
2007
Earlier work this paper cites.
T. Kiesel, W. Vogel, V. Parigi, A. Zavatta, and M. Bellini, Physical Review A 78
Original
2008
Earlier work this paper cites.
J. Řeháček, D. Mogilevtsev, and Z. Hradil, New Journal of Physics 10
2008
Earlier work this paper cites.
R. A. Bertlmann and P. Krammer, Journal of Physics A: Mathematical and Theoretical 41
Original
2008
Earlier work this paper cites.
M. Grant and S. Boyd, in Recent Advances in Learning and Control , Lecture Notes in Control and Information Sciences, edited by V. Blondel, S. Boyd, and H. Kimura (Springer-Verlag Limited, 2008) pp. 95–110
2008
Earlier work this paper cites.
J. P. Home, D. Hanneke, J. D. Jost, J. M. Amini, D. Leibfried, and D. J. Wineland, Science 325
Original
2009
Earlier work this paper cites.
R. Bianchetti, S. Filipp, M. Baur, J. Fink, M. Göppl, P. Leek, L. Steffen, A. Blais, and A. Wallraff, Physical Review A 80
2009
Earlier work this paper cites.