Non-Gaussianity detection of single-mode rotationally symmetric quantum states via cumulant method

doi:10.1088/1674-1056/ad2506

中国物理B ›› 2024, Vol. 33 ›› Issue (5): 50309-050309.doi: 10.1088/1674-1056/ad2506

Non-Gaussianity detection of single-mode rotationally symmetric quantum states via cumulant method

Shao-Hua Xiang(向少华)†, Li-Jun Huang(黄利军), and Xian-Wu Mi(米贤武)

College of Physics, Electronics and Intelligent Manufacturing, Huaihua University, Huaihua 418008, China

收稿日期:2023-12-09 修回日期:2024-01-21 接受日期:2024-02-02 出版日期:2024-05-20 发布日期:2024-05-20
通讯作者: Shao-Hua Xiang E-mail:shxiang97@163.com
基金资助:
Project supported by the Natural Science Foundation of Hunan Province of China (Grant No. 2021JJ30535).

Non-Gaussianity detection of single-mode rotationally symmetric quantum states via cumulant method

Shao-Hua Xiang(向少华)†, Li-Jun Huang(黄利军), and Xian-Wu Mi(米贤武)

College of Physics, Electronics and Intelligent Manufacturing, Huaihua University, Huaihua 418008, China

Received:2023-12-09 Revised:2024-01-21 Accepted:2024-02-02 Online:2024-05-20 Published:2024-05-20
Contact: Shao-Hua Xiang E-mail:shxiang97@163.com
Supported by:
Project supported by the Natural Science Foundation of Hunan Province of China (Grant No. 2021JJ30535).

摘要/Abstract

摘要： The non-Gaussianity of quantum states incarnates an important resource for improving the performance of continuous-variable quantum information protocols. We propose a novel criterion of non-Gaussianity for single-mode rotationally symmetric quantum states via the squared Frobenius norm of higher-order cumulant matrix for the quadrature distribution function. As an application, we study the non-Gaussianities of three classes of single-mode symmetric non-Gaussian states: a mixture of vacuum and Fock states, single-photon added thermal states, and even/odd Schrödinger cat states. It is shown that such a criterion is faithful and effective for revealing non-Gaussianity. We further extend this criterion to two cases of symmetric multi-mode non-Gaussian states and non-symmetric single-mode non-Gaussian states.

关键词: non-Gaussianity criterion, cumulant matrix, quadrature distribution

Abstract: The non-Gaussianity of quantum states incarnates an important resource for improving the performance of continuous-variable quantum information protocols. We propose a novel criterion of non-Gaussianity for single-mode rotationally symmetric quantum states via the squared Frobenius norm of higher-order cumulant matrix for the quadrature distribution function. As an application, we study the non-Gaussianities of three classes of single-mode symmetric non-Gaussian states: a mixture of vacuum and Fock states, single-photon added thermal states, and even/odd Schrödinger cat states. It is shown that such a criterion is faithful and effective for revealing non-Gaussianity. We further extend this criterion to two cases of symmetric multi-mode non-Gaussian states and non-symmetric single-mode non-Gaussian states.

Key words: non-Gaussianity criterion, cumulant matrix, quadrature distribution

中图分类号: (Quantum information)

03.67.-a

03.65.Ta (Foundations of quantum mechanics; measurement theory) 42.50.Dv (Quantum state engineering and measurements)

Shao-Hua Xiang(向少华), Li-Jun Huang(黄利军), and Xian-Wu Mi(米贤武). Non-Gaussianity detection of single-mode rotationally symmetric quantum states via cumulant method[J]. 中国物理B, 2024, 33(5): 50309-050309.

Shao-Hua Xiang(向少华), Li-Jun Huang(黄利军), and Xian-Wu Mi(米贤武). Non-Gaussianity detection of single-mode rotationally symmetric quantum states via cumulant method[J]. Chin. Phys. B, 2024, 33(5): 50309-050309.

参考文献

[1] Opatrný T, Kurizki G and Welsch D G 2000 Phys. Rev. A 61 032302
[2] Cochrane P T, Ralph T C and Milburn G J 2002 Phys. Rev. A 65 062306
[3] Olivares S, Paris M G A and Bonifacio R 2003 Phys. Rev. A 67 032314
[4] Dell’Anno F, Siena S De, Albano L and Illuminati F 2007 Phys. Rev. A 76 022301
[5] Huang P, He G, Fang J and Zeng G 2013 Phys. Rev. A 87 012317
[6] Cerf N J, Krüger O, Navez P, Werner R F and Wolf M M 2005 Phys. Rev. Lett. 95 070501
[7] Genoni M G, Paris M G A and Banaszek K 2007 Phys. Rev. A 76 042327
[8] Genoni M G and Paris M G A 2010 Phys. Rev. A 82 052341
[9] Ivan J S, Kumar M S and Simon R 2012 Quant. Inf. Proc. 11 853
[10] Ghiu I, Marian P and Marian T A 2013 Phys. Scr. T153 014028
[11] Genoni M G, Paris M G A and Banaszek K 2008 Phys. Rev. A 78 060303
[12] Park J, Lee J, Baek K and Nha H 2021 Phys. Rev. A 104 032415
[13] Fu S, Luo S and Zhang Y 2020 Phys. Rev. A 101 012125
[14] Olsen M K and Corney J F 2013 Phys. Rev. A 87 033839
[15] Corney J F and Olsen M K 2015 Phys. Rev. A 91 023824
[16] Xiang S H and Song K H 2015 Eur. Phys. J. D 69 260
[17] Xiang S H, Wen W, Zhao Y J and Song K H 2016 Phys. Rev. A 93 062119
[18] Xiang S H and Song K H 2018 Eur. Phys. J. D 72 185
[19] Xiang S H, Wen W, Zhao Y J and Song K H 2018 Phys. Rev. A 97 042303
[20] Xiang C, Zhao Y J and Xiang S H 2019 Phys. Scr. 94 115101
[21] Yamamoto Y and Kudo S 2017 JSIAM Lett. 9 9
[22] Juhasz T and Mazziotti D A 2006 J. Chem. Phys. 125 174105
[23] Skolnik J T and Mazziotti D A 2013 Phys. Rev. A 88 032517
[24] Yao Y, Dong G H, Xiao X and Sun C P 2016 Sci. Rep. 6 32010
[25] Vogel K and Risken H 1989 Phys. Rev. A 40 2847
[26] Xiang C, Li S S, Wen S S and Xiang S H 2022 Chin. Phys. B 31 030306
[27] Xiang S H, Li S S and Mi X W 2023 Chin. Phys. B 32 050309
[28] Agarwal G S and Tara K 1992 Phys. Rev. A 46 485
[29] Zavatta A, Parigi V and Bellini M 2007 Phys. Rev. A 75 052106
[30] Bužek V, Vidiella-Barranco A and Knight P L 1992 Phys. Rev. A 45 6570
[31] Xia Y J and Guo G C 1989 Phys. Lett. A 136 281
[32] Li F L, Li H R, Zhang J X and Zhu S Y 2002 Phys. Rev. A 66 024302
[33] Cheong Y W, Kim H and Lee H W 2004 Phys. Rev. A 70 032327
[34] Heid M and Lütkenhaus N 2007 Phys. Rev. A 76 022313
[35] Vogel W and Sperling J 2014 Phys. Rev. A 89 052302
[36] Jeong H and An N B 2006 Phys. Rev. A 74 022104
[37] Zhang Y and Luo S L2020 Phys. Scr. 95 035101
[38] Luis A and Monroy L 2017 Phys. Rev. A 96 063802
[39] Kitagawa M and Yamamoto Y 1986 Phys. Rev. A 34 3974
[40] Ould-Baba H, Robin V and Antoni J 2015 Linear Algebra Appl. 485 392
[41] Miki D, Matsumura A and Yamamoto K 2022 Phys. Rev. D 105 026011
[42] Lvovsky A I and Raymer M G 2009 Rev. Mod. Phys. 81 299
[43] Park J, Lu Y, Lee J, Shen Y, Zhang K, Zhang S, Zubairy M S, Kim K and Nha H 2017 Proc. Natl. Acad. Sci. USA 114 891
[44] Roos C, Zeiger T, Rohde H, Nagerl H C, Eschner J, Leibfried D, Schmidt-Kaler F and Blatt R 1999 Phys. Rev. Lett. 83 4713
[45] Yurke B and Stoler D 1986 Phys. Rev. Lett. 57 13
[46] Hacker B, Welte S, Daiss S, Shaukat A, Ritter S, Li L and Rempe G 2019 Nat. Photon. 13 110
[47] Kiesel T, Vogel W, Bellini M and Zavatta A 2011 Phys. Rev. A 83 03211

Non-Gaussianity detection of single-mode rotationally symmetric quantum states via cumulant method

Non-Gaussianity detection of single-mode rotationally symmetric quantum states via cumulant method

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