On a differential geometric viewpoint of Jaynes' MaxEnt method and its quantum extension

S. A. Ali; C. Cafaro; A. Giffin; C. Lupo; S. Mancini

doi:10.1063/1.3703628

On a differential geometric viewpoint of Jaynes' MaxEnt method and its quantum extension

S. A. Ali
, C. Cafaro
, A. Giffin
, C. Lupo
, S. Mancini

Nanoscale Science and Engineering

University at Albany

Albany College of Pharmacy
International Institute for Theoretical Physics and Mathematics Einstein-Galilei
Princeton University
University of Camerino

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

7 Scopus citations

Abstract

We present a differential geometric viewpoint of the quantum MaxEnt estimate of a density operator when only incomplete knowledge encoded in the expectation values of a set of quantum observables is available. Finally, the additional possibility of considering some prior bias towards a certain density operator (the prior) is taken into account and the unsolved issues with its quantum relative entropic inference criterion are pointed out.

Original language	English
Title of host publication	Bayesian Inference and Maximum Entropy Methods in Science and Engineering - 31st International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, MaxEnt 2011
Pages	120-128
Number of pages	9
DOIs	https://doi.org/10.1063/1.3703628
State	Published - 2012
Event	31st International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, MaxEnt 2011 - Waterloo, ON, Canada Duration: Jul 9 2011 → Jul 16 2011

Publication series

Name	AIP Conference Proceedings
Volume	1443

Conference

Conference	31st International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, MaxEnt 2011
Country/Territory	Canada
City	Waterloo, ON
Period	07/9/11 → 07/16/11

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10.1063/1.3703628

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Ali, S. A., Cafaro, C., Giffin, A., Lupo, C., & Mancini, S. (2012). On a differential geometric viewpoint of Jaynes' MaxEnt method and its quantum extension. In Bayesian Inference and Maximum Entropy Methods in Science and Engineering - 31st International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, MaxEnt 2011 (pp. 120-128). (AIP Conference Proceedings; Vol. 1443). https://doi.org/10.1063/1.3703628

Ali, S. A. ; Cafaro, C. ; Giffin, A. et al. / On a differential geometric viewpoint of Jaynes' MaxEnt method and its quantum extension. Bayesian Inference and Maximum Entropy Methods in Science and Engineering - 31st International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, MaxEnt 2011. 2012. pp. 120-128 (AIP Conference Proceedings).

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abstract = "We present a differential geometric viewpoint of the quantum MaxEnt estimate of a density operator when only incomplete knowledge encoded in the expectation values of a set of quantum observables is available. Finally, the additional possibility of considering some prior bias towards a certain density operator (the prior) is taken into account and the unsolved issues with its quantum relative entropic inference criterion are pointed out.",

author = "Ali, \{S. A.\} and C. Cafaro and A. Giffin and C. Lupo and S. Mancini",

year = "2012",

doi = "10.1063/1.3703628",

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booktitle = "Bayesian Inference and Maximum Entropy Methods in Science and Engineering - 31st International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, MaxEnt 2011",

note = "31st International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, MaxEnt 2011 ; Conference date: 09-07-2011 Through 16-07-2011",

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Ali, SA, Cafaro, C, Giffin, A, Lupo, C & Mancini, S 2012, On a differential geometric viewpoint of Jaynes' MaxEnt method and its quantum extension. in Bayesian Inference and Maximum Entropy Methods in Science and Engineering - 31st International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, MaxEnt 2011. AIP Conference Proceedings, vol. 1443, pp. 120-128, 31st International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, MaxEnt 2011, Waterloo, ON, Canada, 07/9/11. https://doi.org/10.1063/1.3703628

On a differential geometric viewpoint of Jaynes' MaxEnt method and its quantum extension. / Ali, S. A.; Cafaro, C.; Giffin, A. et al.
Bayesian Inference and Maximum Entropy Methods in Science and Engineering - 31st International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, MaxEnt 2011. 2012. p. 120-128 (AIP Conference Proceedings; Vol. 1443).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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PY - 2012

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AB - We present a differential geometric viewpoint of the quantum MaxEnt estimate of a density operator when only incomplete knowledge encoded in the expectation values of a set of quantum observables is available. Finally, the additional possibility of considering some prior bias towards a certain density operator (the prior) is taken into account and the unsolved issues with its quantum relative entropic inference criterion are pointed out.

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Ali SA, Cafaro C, Giffin A, Lupo C, Mancini S. On a differential geometric viewpoint of Jaynes' MaxEnt method and its quantum extension. In Bayesian Inference and Maximum Entropy Methods in Science and Engineering - 31st International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, MaxEnt 2011. 2012. p. 120-128. (AIP Conference Proceedings). doi: 10.1063/1.3703628

On a differential geometric viewpoint of Jaynes' MaxEnt method and its quantum extension

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