3 Maximum-Likelihood Methodsin Quantum Mechanics

Hradil, Zdeněk; Řeháček, Jaroslav; Fiurášek, Jaromír; Ježek, Miroslav

doi:10.1007/978-3-540-44481-7_3

Zdeněk Hradil¹,
Jaroslav Řeháček¹,
Jaromír Fiurášek^1,2 &
…
Miroslav Ježek¹

Part of the book series: Lecture Notes in Physics ((LNP,volume 649))

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Abstract

Maximum Likelihood estimation is a versatile tool covering wide range of applications, but its benefits are apparent particularly in the quantum domain. For a given set of measurements, the most likely state is estimated. Though this problem is nonlinear, it can be effectively solved by an iterative algorithm exploiting the convexity of the likelihood functional and the manifold of density matrices. This formulation fully replaces the inverse Radon transformation routinely used for tomographic reconstructions. Moreover, it provides the most efficient estimation strategy saturating the Cramer-Rao lower bound asymptotically. In this sense it exploits the acquired data set in the optimal way and minimizes the artifacts associated with the reconstruction procedure. The idea of maximum likelihood reconstruction is further extended to the estimation of quantum processes, measurements, and discrimination between quantum states. This technique is well suited for future applications in quantum information science due to its ability to quantify very subtle and fragile quantum effects.

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Authors and Affiliations

Department of Optics, Palacky University, Olomouc, Czech Republic
Zdeněk Hradil, Jaroslav Řeháček, Jaromír Fiurášek & Miroslav Ježek
Ecole Polytechnique, CP 165, Université Libre de Bruxelles, 1050 Bruxelles, Belgium
Jaromír Fiurášek

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Zdeněk Hradil
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Jaroslav Řeháček
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Jaromír Fiurášek
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Miroslav Ježek
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Matteo Paris Jaroslav Řeháček

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Hradil, Z., Řeháček, J., Fiurášek, J., Ježek, M. 3 Maximum-Likelihood Methodsin Quantum Mechanics. In: Paris, M., Řeháček, J. (eds) Quantum State Estimation. Lecture Notes in Physics, vol 649. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-44481-7_3

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DOI: https://doi.org/10.1007/978-3-540-44481-7_3
Published: 18 August 2004
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-22329-0
Online ISBN: 978-3-540-44481-7
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