|
|
|
Algorithm for evaluating distance-based entanglement measures |
| Yixuan Hu(胡奕轩)1, Ye-Chao Liu(刘烨超)2,1,†, and Jiangwei Shang(尚江伟)1,‡ |
1. Key Laboratory of Advanced Optoelectronic Quantum Architecture and Measurement of Ministry of Education, School of Physics, Beijing Institute of Technology, Beijing 100081, China;
2. Naturwissenschaftlich-Technische Fakultät, Universität Siegen, Siegen 57068, Germany |
|
|
|
|
Abstract Quantifying entanglement in quantum systems is an important yet challenging task due to its NP-hard nature. In this work, we propose an efficient algorithm for evaluating distance-based entanglement measures. Our approach builds on Gilbert's algorithm for convex optimization, providing a reliable upper bound on the entanglement of a given arbitrary state. We demonstrate the effectiveness of our algorithm by applying it to various examples, such as calculating the squared Bures metric of entanglement as well as the relative entropy of entanglement for GHZ states, W states, Horodecki states, and chessboard states. These results demonstrate that our algorithm is a versatile and accurate tool that can quickly provide reliable upper bounds for entanglement measures.
|
Received: 31 March 2023
Revised: 09 May 2023
Accepted manuscript online: 16 May 2023
|
|
PACS:
|
03.67.-a
|
(Quantum information)
|
| |
03.67.Mn
|
(Entanglement measures, witnesses, and other characterizations)
|
| |
02.60.Pn
|
(Numerical optimization)
|
|
| Fund: Project supported by the National Natural Science Foundation of China (Grant Nos.12175014 and 92265115) and the National Key Research and Development Program of China (Grant No.2022YFA1404900). Y. C. Liu is also supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation, project numbers 447948357 and 440958198) and the Sino-German Center for Research Promotion (Project M-0294). |
Corresponding Authors:
Ye-Chao Liu, Jiangwei Shang
E-mail: ye-chao.liu@uni-siegen.de;jiangwei.shang@bit.edu.cn
|
Cite this article:
Yixuan Hu(胡奕轩), Ye-Chao Liu(刘烨超), and Jiangwei Shang(尚江伟) Algorithm for evaluating distance-based entanglement measures 2023 Chin. Phys. B 32 080307
|
[1] Horodecki M 2001 Quantum Inf. Comput. 1 3
[2] Horodecki R, Horodecki P, Horodecki M and Horodecki K 2009 Rev. Mod. Phys. 81 865
[3] Peres A 1996 Phys. Rev. Lett. 77 1413
[4] Chen K and Wu L A 2003 Quantum Inf. Comput. 3 193
[5] Rudolph O 2005 Quantum Inf. Process. 4 219
[6] Horodecki M, Horodecki P and Horodecki R 1996 Phys. Lett. A 223 1
[7] Terhal B M 2000 Phys. Lett. A 271 319
[8] Lewenstein M, Kraus B, Cirac J I and Horodecki P 2000 Phys. Rev. A 62 052310
[9] Bruβ D, Cirac J I, Horodecki P, Hulpke F, Kraus B, Lewenstein M and Sanpera A 2002 J. Mod. Opt. 49 1399
[10] Yu S and Liu N L 2005 Phys. Rev. Lett. 95 150504
[11] Gühne O, Mechler M, Tóth G and Adam P 2006 Phys. Rev. A 74 010301
[12] Spedalieri F M 2007 Phys. Rev. A 76 032318
[13] Navascués M, Owari M and Plenio M B 2009 Phys. Rev. Lett. 103 160404
[14] Kampermann H, Gühne O, Wilmott C and Bruβ D 2012 Phys. Rev. A 86 032307
[15] Gilbert E G 1966 SIAM J. Control Optim. 4 61
[16] Brierley S, Navascues M and Vertesi T 2017 arXiv: 1609.05011
[17] Shang J and Gühne O 2018 Phys. Rev. Lett. 120 050506
[18] Wieśniak M, Pandya P, Sakarya O and Woloncewicz B 2020 Quantum Rep. 2 49
[19] Pandya P, Sakarya O and Wieśniak M 2020 Phys. Rev. A 102 012409
[20] Plenio M B and Virmani S 2007 Quantum Inf. Comput. 7 1
[21] Uhlmann A 1998 Open Sys. Inf. Dyn. 5 209
[22] Vidal G, Jonathan D and Nielsen M A 2000 Phys. Rev. A 62 012304
[23] Vedral V, Plenio M B, Rippin M A and Knight P L 1997 Phys. Rev. Lett. 78 2275
[24] Vedral V and Plenio M B 1998 Phys. Rev. A 57 1619
[25] Gurvits L and Barnum H 2003 Phys. Rev. A 68 042312
[26] Gharibian S 2010 Quantum Inf. Comput. 10 343
[27] Dür W, Vidal G and Cirac J I 2000 Phys. Rev. A 62 062314
[28] Acín A, Bruβ D, Lewenstein M and Sanpera A 2001 Phys. Rev. Lett. 87 040401
[29] Schumacher B and Westmoreland M D 2000 arXiv: quant-ph/0004045[quant-ph]
[30] Vedral V 2002 Rev. Mod. Phys. 74 197
[31] Brandão F G S L and Plenio M B 2008 Nat. Phys. 4 873
[32] Chen Z H, Ma Z H, Gühne O and Severini S S 2012 Phys. Rev. Lett. 109 200503
[33] Horodecki P 1997 Phys. Lett. A 232 333
[34] Bruβ D and Peres A 2000 Phys. Rev. A 61 030301 |
| 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
|
|
|
