Please wait a minute...
Chin. Phys. B, 2014, Vol. 23(9): 090305    DOI: 10.1088/1674-1056/23/9/090305
GENERAL Prev   Next  

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
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.
Keywords:  quantum Chernoff metric      Hellinger distance      perturbation expansion  
Received:  17 January 2014      Revised:  26 March 2014      Accepted manuscript online: 
PACS:  03.65.Ta (Foundations of quantum mechanics; measurement theory)  
  03.67.-a (Quantum information)  
Fund: 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).
Corresponding Authors:  Wang Xiao-Guang     E-mail:  xgwang@zimp.zju.edu.cn

Cite this article: 

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 2014 Chin. Phys. B 23 090305

[1] Helstrom C W 1976 Quantum Detection and Estimation Theory
[2] Holevo A S 1982 Probabilistic and Statistical Aspects of Quantum Theory
[3] Malley J D and Hornstein J 1993 Statistical Science 8 433
[4] Cover T M and Thomas J A 2006 Elements of Information Theory
[5] Chernoff H 1925 Ann. Math. Stat. 23 493
[6] Fuchs C A 1996 arXiv:quant-ph 9601020
[7] Fuchs C A and van de Graaf J 1999 IEEE Trans. Inf. Theory 45 1216
[8] Nussbaum M and Szkola A 2009 Annals of Statistics 37 1040
[9] Audenaert K M R, Calsamiglia J, Muñoz-Tapia R, Bagan E, Masanes L, Acin A and Verstraete F 2007 Phys. Rev. Lett. 98 160501
[10] Pirandola S and Lloyd S 2008 Phys. Rev. A 78 012331
[11] Boca M, Ghiu I, Marian P and Marian T A 2009 Phys. Rev. A 79 014302
[12] Calsamiglia J, de Vicente J I, Muñoz-Tapia R and Bagan E 2010 Phys. Rev. Lett. 105 080504
[13] Sentís G, Bagan E, Calsamiglia J and Muñoz-Tapia R 2010 Phys. Rev. A 82 042312
[14] Higgins B L, Doherty A C, Bartlett S D, Pryde G J and Wiseman H M 2011 Phys. Rev. A 83 052314
[15] Duan R Y, Feng Y and Ying M S 2009 Phys. Rev. Lett. 103 210501
[16] Invernizzi C, Paris M G A and Pirandola S 2011 Phys. Rev. A 84 022334
[17] Pirandola S 2011 Phys. Rev. Lett. 106 090504
[18] Spedalieri G, Lupo C, Mancini S, Braunstein S L and Pirandola S 2012 Phys. Rev. A 86 012315
[19] Nair R 2011 Phys. Rev. A 84 032312
[20] Tan S H, Erkmen B I, Giovannetti V, Guha S, Lloyd S, Maccone L, Pirandola S and Shapiro J H 2008 Phys. Rev. Lett. 101 253601
[21] Shapiro J H 2009 Phys. Rev. A 80 022320
[22] Zanardi P, Venuti L C and Giorda P 2007 Phys. Rev. A 76 062318
[23] Abasto D F, Jacobson N T and Zanardi P 2008 Phys. Rev. A 77 022327
[24] Invernizzi C and Paris M G A 2010 J. Mod. Opt. 57 198
[25] Calsamiglia J, Muñoz-Tapia R, Masanes L, Acin A and Bagan E 2008 Phys. Rev. A 77 032311
[26] Hübner M 1992 Phys. Lett. A 163 239
[27] Sommers H J and Zyczkowski K 2003 J. Phys. A: Math. Gen. 36 10083
[28] Zanardi P, Giorda P and Cozzini M 2007 Phys. Rev. Lett. 99 100603
[29] Luo S L and Zhang Q 2004 Phys. Rev. A 69 032106
[30] Wigner E P and Yanase M M 1963 Proc. Natl. Acad. Sci. USA 49 910
[31] Luo S L 2003 Phys. Rev. Lett. 91 180403
[32] Sun H G, Liu W F and Li C J 2011 Chin. Phys. B 20 090301
[33] Sun H G, Zhang L H, Liu W F and Li C J 2012 Chin. Phys. B 21 010301
[34] Paris M G A 2009 Int. J. Quan. Info. 7 125
[35] Braunstein S L and Caves C M 1994 Phys. Rev. Lett. 72 3439
[36] Petz D 1996 Linear Algebra Appl. 244 81
[37] Tsang M 2012 Phys. Rev. Lett. 108 230401
[38] Zhong W, Sun Z, Ma J, Wang X G and Nori F 2013 Phys. Rev. A 87 022337
[39] Dittmann J 1999 J. Phys. A: Math. Theor. 32 2663
[1] An adiabatic quantum optimization for exact cover 3 problem
Zhang Ying-Yu (张映玉), Xu Li-Li (许丽莉), Li Jun-Qing (李俊青). Chin. Phys. B, 2014, 23(3): 030308.
[2] Vertically forced surface wave in weakly viscous fluids bounded in a circular cylindrical vessel
Jian Yong-Jun (菅永军), E Xue-Quan (鄂学全). Chin. Phys. B, 2004, 13(8): 1191-1200.
No Suggested Reading articles found!