|
|
The stabilizer for n-qubit symmetric states |
Xian Shi(石现)1,2,3 |
1 Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China;
2 University of Chinese Academy of Sciences, Beijing 100049, China;
3 UTS-AMSS Joint Research Laboratory for Quantum Computation and Quantum Information Processing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China |
|
|
Abstract The stabilizer group for an n-qubit state|φ> is the set of all invertible local operators (ILO) g=g1⊗ g2⊗ …⊗ gn, gi∈ GL(2,C) such that|φ>=g|φ>. Recently, Gour et al.[Gour G, Kraus B and Wallach N R 2017 J. Math. Phys. 58 092204] presented that almost all n-qubit states|Ψ〉 own a trivial stabilizer group when n ≥ 5. In this article, we consider the case when the stabilizer group of an n-qubit symmetric pure state|Ψ> is trivial. First we show that the stabilizer group for an n-qubit symmetric pure state|φ> is nontrivial when n ≤ 4. Then we present a class of n-qubit symmetric states|φ> with a trivial stabilizer group when n ≥ 5. Finally, we propose a conjecture and prove that an n-qubit symmetric pure state owns a trivial stabilizer group when its diversity number is bigger than 5 under the conjecture we make, which confirms the main result of Gour et al. partly.
|
Received: 30 April 2018
Revised: 01 July 2018
Accepted manuscript online:
|
PACS:
|
03.67.Mn
|
(Entanglement measures, witnesses, and other characterizations)
|
|
03.65.Ud
|
(Entanglement and quantum nonlocality)
|
|
Fund: Project partially supported by the National Key Research and Development Program of China (Grant No. 2016YFB1000902), the National Natural Science Foundation of China (Grant Nos. 61232015 and 61621003), the Knowledge Innovation Program of the Chinese Academy of Sciences (CAS), and Institute of Computing Technology of CAS. |
Corresponding Authors:
Xian Shi
E-mail: shixian01@gmail.com
|
Cite this article:
Xian Shi(石现) The stabilizer for n-qubit symmetric states 2018 Chin. Phys. B 27 100311
|
[1] |
Horodecki R, Horodecki M and Horodecki K 2009 Rev. Mod. Phys. 81 865
|
[2] |
Bennett C H, Brassard G, Crépeau C, Jozsa R, Peres A and Wootters W K 1993 Phys. Rev. Lett. 70 1895
|
[3] |
Bennett C H and Wiesner S 1992 Phys. Rev. Lett. 69 2881
|
[4] |
Dür W, Vidal G and Cirac J I 2000 Phys. Rev. A 62 062314
|
[5] |
Walter M, Doran B, Gross D and Christandl M 2013 Science 340 1205
|
[6] |
Zhang T G, Zhao M J and Huang X F 2016 J. Phys. A:Math. Theor. 49 405301
|
[7] |
Chen L and Chen Y X 2006 Phys. Rev. A 74 062310
|
[8] |
Lamata L, León J, Salgado D and Solano E 2006 Phys. Rev. A 74 052336
|
[9] |
Li X R and Li D F 2012 Phys. Rev. Lett. 108 180502
|
[10] |
Gour G and Wallach N R 2013 Phys. Rev. Lett. 111 060502
|
[11] |
Gour G and Wallach N R 2011 New J. Phys. 13 073013
|
[12] |
Gour G, Kraus B and Wallach N R 2017 J. Math. Phys. 58 092204
|
[13] |
Sauerwein D, Wallach N R, Gour G and Kraus B 2018 Phys. Rev. X 8 031020
|
[14] |
Bastin T, Krins S, Mathonet P, Godefroid M, Lamata L and Solano E 2009 Phys. Rev. Lett. 103 070503
|
[15] |
Mathonet P, Krins S, Godefroid M, Lamata L, Solano E and Bastin T 2010 Phys. Rev. A 81 052315
|
[16] |
Migda P, Rodriguez J and Lewenstein M 2013 Phys. Rev. A 88 012335
|
[17] |
Ribeiro P and Mosseri R 2011 Phys. Rev. Lett. 106 180502
|
[18] |
Baguette D, Bastin T and Martin J 2014 Phys. Rev. A 90 032314
|
[19] |
Majorana E 1932 Nuovo Cimento 9 43
|
[20] |
Needham N 1999 Visual Complex Analysis (Oxford:Clarendon Press)
|
[21] |
Aullbach M 2012 Int. J. Quantum Inform. 10 1230004
|
[22] |
Gour G and Wallach N R 2010 J. Math. Phys. 51 112201
|
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
|
|
|