Score operators of a qubit with applications

Score operators of a qubit with applications The score operators of a quantum system are the symmetric logarithmic derivatives of the system’s parametrically defined quantum state. Score operators are central to the calculation of the quantum Fisher information (QFI) associated with the state of the system, and the QFI determines the maximum precision with which the state parameters can be estimated. We give a simple, explicit expression for score operators of a qubit and apply this expression in a series of settings. We treat in detail the task of identifying a quantum Pauli channel from the state of its qubit output, and we show that a “balanced” probe state is highly robust for this purpose. The QFI for this task is a matrix, and we study its determinant, for which we establish a Cramér-Rao inequality. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

Score operators of a qubit with applications

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Publisher
Springer US
Copyright
Copyright © 2010 by Springer Science+Business Media, LLC
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/s11128-010-0170-5
Publisher site
See Article on Publisher Site

Abstract

The score operators of a quantum system are the symmetric logarithmic derivatives of the system’s parametrically defined quantum state. Score operators are central to the calculation of the quantum Fisher information (QFI) associated with the state of the system, and the QFI determines the maximum precision with which the state parameters can be estimated. We give a simple, explicit expression for score operators of a qubit and apply this expression in a series of settings. We treat in detail the task of identifying a quantum Pauli channel from the state of its qubit output, and we show that a “balanced” probe state is highly robust for this purpose. The QFI for this task is a matrix, and we study its determinant, for which we establish a Cramér-Rao inequality.

Journal

Quantum Information ProcessingSpringer Journals

Published: Mar 10, 2010

References

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