Derivation of quantum Chernoff metric with perturbation expansion method

doi:10.1088/1674-1056/23/9/090305

›› 2014, Vol. 23 ›› Issue (9): 90305-090305.doi: 10.1088/1674-1056/23/9/090305

Derivation of quantum Chernoff metric with perturbation expansion method

钟伟, 马健, 刘京, 王晓光

Zhejiang Institute of Modern Physics, Zhejiang University, Hangzhou 310027, China

收稿日期:2014-01-17 修回日期:2014-03-26 出版日期:2014-09-15 发布日期:2014-09-15
基金资助:
Project supported by the National Basic Research Program of China (Grant No. 2012CB921602) and the National Natural Science Foundation of China (Grant Nos. 11025527 and 10935010).

Derivation of quantum Chernoff metric with perturbation expansion method

Zhong Wei (钟伟), Ma Jian (马健), Liu Jing (刘京), Wang Xiao-Guang (王晓光)

Zhejiang Institute of Modern Physics, Zhejiang University, Hangzhou 310027, China

Received:2014-01-17 Revised:2014-03-26 Online:2014-09-15 Published:2014-09-15
Contact: Wang Xiao-Guang E-mail:xgwang@zimp.zju.edu.cn
Supported by:
Project supported by the National Basic Research Program of China (Grant No. 2012CB921602) and the National Natural Science Foundation of China (Grant Nos. 11025527 and 10935010).

摘要/Abstract

摘要： We investigate a measure of distinguishability defined by the quantum Chernoff bound, which naturally induces the quantum Chernoff metric over a manifold of quantum states. Based on a quantum statistical model, we alternatively derive this metric by means of perturbation expansion. Moreover, we show that the quantum Chernoff metric coincides with the infinitesimal form of the quantum Hellinger distance, and reduces to the variant version of the quantum Fisher information for the single-parameter case. We also give the exact form of the quantum Chernoff metric for a qubit system containing a single parameter.

关键词: quantum Chernoff metric, Hellinger distance, perturbation expansion

Abstract: We investigate a measure of distinguishability defined by the quantum Chernoff bound, which naturally induces the quantum Chernoff metric over a manifold of quantum states. Based on a quantum statistical model, we alternatively derive this metric by means of perturbation expansion. Moreover, we show that the quantum Chernoff metric coincides with the infinitesimal form of the quantum Hellinger distance, and reduces to the variant version of the quantum Fisher information for the single-parameter case. We also give the exact form of the quantum Chernoff metric for a qubit system containing a single parameter.

Key words: quantum Chernoff metric, Hellinger distance, perturbation expansion

中图分类号: (Foundations of quantum mechanics; measurement theory)

03.65.Ta

03.67.-a (Quantum information)

钟伟, 马健, 刘京, 王晓光. Derivation of quantum Chernoff metric with perturbation expansion method[J]. , 2014, 23(9): 90305-090305.

Zhong Wei (钟伟), Ma Jian (马健), Liu Jing (刘京), Wang Xiao-Guang (王晓光). Derivation of quantum Chernoff metric with perturbation expansion method[J]. Chin. Phys. B, 2014, 23(9): 90305-090305.

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Derivation of quantum Chernoff metric with perturbation expansion method

Derivation of quantum Chernoff metric with perturbation expansion method

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