|
|
|
Bounds on positive operator-valued measure based coherence of superposition |
| Meng-Li Guo(郭梦丽)1, Jin-Min Liang(梁津敏)1, Bo Li(李波)2, Shao-Ming Fei(费少明)1,3,†, and Zhi-Xi Wang(王志玺)1,‡ |
1 School of Mathematical Sciences, Capital Normal University, Beijing 100048, China;
2 School of Computer and Computing Science, Hangzhou City University, Hangzhou 310015, China;
3 Max-Planck-Institute for Mathematics in the Sciences, Leipzig 04103, Germany |
|
|
|
|
Abstract Quantum coherence is a fundamental feature of quantum physics and plays a significant role in quantum information processing. By generalizing the resource theory of coherence from von Neumann measurements to positive operator-valued measures (POVMs), POVM-based coherence measures have been proposed with respect to the relative entropy of coherence, the l1 norm of coherence, the robustness of coherence and the Tsallis relative entropy of coherence. We derive analytically the lower and upper bounds on these POVM-based coherence of an arbitrary given superposed pure state in terms of the POVM-based coherence of the states in superposition. Our results can be used to estimate range of quantum coherence of superposed states. Detailed examples are presented to verify our analytical bounds.
|
Received: 20 November 2022
Revised: 31 January 2023
Accepted manuscript online: 08 February 2023
|
|
PACS:
|
03.65.Aa
|
(Quantum systems with finite Hilbert space)
|
| |
03.67.-a
|
(Quantum information)
|
| |
03.67.Mn
|
(Entanglement measures, witnesses, and other characterizations)
|
|
| Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 12075159, 12171044, and 12175147), the Natural Science Foundation of Beijing (Grant No. Z190005), the Academician Innovation Platform of Hainan Province, Shenzhen Institute for Quantum Science and Engineering, and Southern University of Science and Technology (Grant No. SIQSE202001). |
Corresponding Authors:
Shao-Ming Fei, Zhi-Xi Wang
E-mail: feishm@cnu.edu.cn;wangzhx@cnu.edu.cn
|
Cite this article:
Meng-Li Guo(郭梦丽), Jin-Min Liang(梁津敏), Bo Li(李波), Shao-Ming Fei(费少明), and Zhi-Xi Wang(王志玺) Bounds on positive operator-valued measure based coherence of superposition 2023 Chin. Phys. B 32 050302
|
[1] Jozsa R and Linden N 2003 Proc. R. Soc. A 459 2011
[2] Horodecki R, Horodecki P, Horodecki M and Horodecki K 2009 Rev. Mod. Phys. 81 865
[3] Designolle S, Uola R, Luoma K and Brunner N 2021 Phys. Rev. Lett. 126 220404
[4] Linden N, Popescu S and Smolin J A 2006 Phys. Rev. Lett. 97 100502
[5] Gilad G 2007 Phys. Rev. A 76 052320
[6] Niset J and Cerf N J 2007 Phys. Rev. A 76 042328
[7] Akhtarshenas S J 2011 Phys. Rev. A 83 042306
[8] Baumgratz T, Cramer M and Plenio M B 2014 Phys. Rev. Lett. 113 140401
[9] Streltsov A, Adesso G and Plenio M B 2017 Rev. Mod. Phys. 89 041003
[10] Hu M L, Hu X, Wang J, Peng Y, Zhang Y R and Fan H 2018 Phys. Rep. 762 1-100
[11] Winter A and Yang D 2016 Phys. Rev. Lett. 116 120404
[12] Bu K F, U Singh, Fei S M, Pati A K and Wu J D 2017 Phys. Rev. Lett. 119 150405
[13] Zhao H Q and Yu C S 2018 Sci. Rep. 8 299
[14] Xiong C H, Kumar A and Wu J D 2018 Phys. Rev. A 98 032324
[15] Guo M L, Jin Z X, Li B, Hu B and Fei S M 2020 Quantum Inf. Process. 19 382
[16] Bischof F, Kampermann H and Bruß D 2019 Phys. Rev. Lett 123 110402
[17] Bischof F, Kampermann H and Bruß D 2021 Phys. Rev. A 103 032429
[18] Xu J W, Shao L H and Fei S M 2020 Phys. Rev. A 102 012411
[19] Nielsen M A and Chuang I L 2000 Quantum Computation and Quantum Information(Cambridge: Cambridge University Press) pp. 155– 162
[20] Jin Z X, Yang L M, Fei S M, Li-Jost X, Wang Z X, Long G L and Qiao C F 2021 Sci. China Phys. Mech. Astron. 64 280311
[21] Yue Q L, Liu F, Yu C H, Wang X L and Gao F 2016 arXiv preprint arXiv: 1605.04067
[22] Liu F and Li F 2016 Quantum Inf. Process. 15 4203
[23] Yue Q L, Gao F, Wen Q Y and Zhang W W 2017 Sci. Rep. 7 4006
[24] Yuwen S S, Shao L H and Xi Z J 2019 Commun. Theor. Phys. 71 9
[25] Singh U, Bera M N, Misra A and Pati A K 2015 arXiv preprint arXiv: 1506.08186
[26] Xu J W, Zhang L and Fei S M 2022 Quantum Inf. Process. 21 39
[27] Piani M, Cianciaruso M, Bromley T R, Napoli C, Johnston N and Adesso G 2016 Phys. Rev. A 93 042107
[28] Rastegin A E 2016 Phys. Rev. A 93 032136
[29] Rastegin A E 2013 Eur. Phys. J. D 67 269
[30] Audenaert K M 1990 Lett. Math Phys. 19 167
[31] Peres A 2006 Quantum Theory: Concepts and Methods (New York: Springer Science & Business Media) pp. 55–60
[32] Decker T, Janzing D and Rötteler M 2005 J. Math. Phys. 46 012104
[33] Roy P and Qureshi T 2019 Phys. Scr. 94 095004
[34] Chen X, Deng Y, Liu S, Pramanik T, Mao J, Bao J, Zhai C, Yuan H, Guo J, Fei S M, Tang B, Yang Y, Li Z, He Q, Gong Q and Wang J 2021 Nat. Commun. 12 2712 |
| No Suggested Reading articles found! |
|
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
Cited |
|
|
|
|
Altmetric
|
|
blogs
Facebook pages
Wikipedia page
Google+ users
|
Online attention
Altmetric calculates a score based on the online attention an article receives. Each coloured thread in the circle represents a different type of online attention. The number in the centre is the Altmetric score. Social media and mainstream news media are the main sources that calculate the score. Reference managers such as Mendeley are also tracked but do not contribute to the score. Older articles often score higher because they have had more time to get noticed. To account for this, Altmetric has included the context data for other articles of a similar age.
View more on Altmetrics
|
|
|
