Bayes cost of parameter estimation for a quantum system interacting with an environment

Bayes cost of parameter estimation for a quantum system interacting with an environment The Bayes cost of parameter estimation is studied for a quantum system which is influenced by an external environment, where the cost function is assumed to be a quadratic function of a difference between true and estimated values. When the reduced time evolution of a quantum system is determined by the time-dependent Lindblad equation, it is found how the Bayes cost changes with time. The Bayes cost increases monotonously with time for the Markovian environment, while it shows an oscillatory behavior for the non-Markovian environment due to the memory effect. Furthermore, in order to investigate how initial correlation between quantum system and environment, an analytic expression of the Bayes cost is derived for a qubit-oscillator system. It is found for both Markovian and non-Markovian environments that the Bayes cost can take a value smaller than the initial one in the presence of the initial correlation. The decrease in the Bayes cost is due to the backflow of information that is included in the initially correlated part. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

Bayes cost of parameter estimation for a quantum system interacting with an environment

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Publisher
Springer US
Copyright
Copyright © 2016 by Springer Science+Business Media New York
Subject
Physics; Quantum Information Technology, Spintronics; Quantum Computing; Data Structures, Cryptology and Information Theory; Quantum Physics; Mathematical Physics
ISSN
1570-0755
eISSN
1573-1332
D.O.I.
10.1007/s11128-016-1267-2
Publisher site
See Article on Publisher Site

Abstract

The Bayes cost of parameter estimation is studied for a quantum system which is influenced by an external environment, where the cost function is assumed to be a quadratic function of a difference between true and estimated values. When the reduced time evolution of a quantum system is determined by the time-dependent Lindblad equation, it is found how the Bayes cost changes with time. The Bayes cost increases monotonously with time for the Markovian environment, while it shows an oscillatory behavior for the non-Markovian environment due to the memory effect. Furthermore, in order to investigate how initial correlation between quantum system and environment, an analytic expression of the Bayes cost is derived for a qubit-oscillator system. It is found for both Markovian and non-Markovian environments that the Bayes cost can take a value smaller than the initial one in the presence of the initial correlation. The decrease in the Bayes cost is due to the backflow of information that is included in the initially correlated part.

Journal

Quantum Information ProcessingSpringer Journals

Published: Feb 20, 2016

References

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