[en] We propose a detailed study of the geometric entanglement properties of pure symmetric N-qubit states, focusing more particularly on the identification of symmetric states with a high geometric entanglement and how their entanglement behaves asymptotically for large N. We show that much higher geometric entanglement with improved asymptotical behavior can be obtained in comparison with the highly entangled balanced Dicke states studied previously. We also derive an upper bound for the geometric measure of entanglement of symmetric states. The connection with the quantumness of a state is discussed.
Disciplines :
Physics
Author, co-author :
Martin, John ; Université de Liège - ULiège > Département de physique > Spectroscopie atomique et Physique des atomes froids
Giraud, O.
Braun, P. A.
Braun, D.
Bastin, Thierry ; Université de Liège - ULiège > Département de physique > Spectroscopie atomique et Physique des atomes froids
Language :
English
Title :
Multiqubit symmetric states with high geometric entanglement
Publication date :
2010
Journal title :
Physical Review. A, Atomic, molecular, and optical physics
ISSN :
1050-2947
eISSN :
1094-1622
Publisher :
American Physical Society, College Park, United States - Maryland
scite shows how a scientific paper has been cited by providing the context of the citation, a classification describing whether it supports, mentions, or contrasts the cited claim, and a label indicating in which section the citation was made.
Bibliography
M. Nielsen and I. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, UK, 2000);
R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.81.865 81, 865 (2009).
M. B. Plenio and S. Virmani, Quantum Inf. Comput. 7, 1 (2007);
O. Gühne and G. Tóth, Phys. Rep. PRPLCM 0370-1573 10.1016/j.physrep.2009.02.004 474, 1 (2009).
T.-C. Wei and P. M. Goldbart, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.68.042307 68, 042307 (2003);
T.-C. Wei, M. Ericsson, P. M. Goldbart, and W. J. Munro, Quantum Inf. Comput. 4, 252 (2004).
O. Biham, M. A. Nielsen, and T. J. Osborne, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.65.062312 65, 062312 (2002);
Y. Shimoni, D. Shapira, and O. Biham, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.69.062303 69, 062303 (2004).
M. Hayashi, D. Markham, M. Murao, M. Owari, and S. Virmani, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.96.040501 96, 040501 (2006).
M. Hayashi, D. Markham, M. Murao, M. Owari, and S. Virmani, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.77.012104 77, 012104 (2008).
T.-C. Wei, D. Das, S. Mukhopadyay, S. Vishveshwara, and P. M. Goldbart, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.71.060305 71, 060305 (R) (2005).
D. Markham, J. Anders, V. Vedral, M. Murao, and A. Miyake, Euro. Phys. Lett. EULEEJ 0295-5075 10.1209/0295-5075/81/40006 81, 40006 (2008).
R. Orús, S. Dusuel, and J. Vidal, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.101.025701 101, 025701 (2008).
Y. Nakata, D. Markham, and M. Murao, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.79.042313 79, 042313 (2009).
S. Tamaryan, A. Sudbery, and L. Tamaryan, Phys. Rev. A 1050-2947 10.1103/PhysRevA.81.052319 81, 052319 (2010).
D. Markham, A. Miyake, and S. Virmani, New J. Phys. NJOPFM 1367-2630 10.1088/1367-2630/9/6/194 9, 194 (2007);
X. Y. Chen, e-print arXiv: 0909.1603.
L. Tamaryan, D. K. Park, and S. Tamaryan, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.77.022325 77, 022325 (2008);
S. Tamaryan, T.-C. Wei, and D. K. Park, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.80.052315 80, 052315 (2009);
S. Tamaryan, H. Kim, M. S. Kim, K. S. Jang, and D. K. Park, e-print arXiv: 0909.1077.
M. Hayashi, D. Markham, M. Murao, M. Owari, and S. Virmani, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.3271041 50, 122104 (2009).
P. Parashar and S. Rana, e-print arXiv: 0909.4443.
L. Chen, A. Xu, and H. Zhu, e-print arXiv: 0911.1493.
R. Hübener, M. Kleinmann, T.-C. Wei, C. González- Guillén, and O. Gühne, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.80.032324 80, 032324 (2009).
E. Jung, M.-R. Hwang, H. Kim, M.-S. Kim, D. K. Park, J.-W. Son, and S. Tamaryan, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.77.062317 77, 062317 (2008).
O. Giraud, P. Braun, and D. Braun, New J. Phys. 1367-2630 10.1088/1367-2630/12/6/063005 12, 063005 (2010).
E. Majorana, Nuovo Cimento NUCIAD 0029-6341 10.1007/BF02960953 9, 43 (1932).
R. H. Dicke, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.93.99 93, 99 (1954).
See, for example, I. Bengtsson and K. Zyczkowski, Geometry of Quantum States: An Introduction to Quantum Entanglement (Cambridge University Press, Cambridge, UK, 2006).
T. Bastin, C. Thiel, J. von Zanthier, L. Lamata, E. Solano, and G. S. Agarwal, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.102.053601 102, 053601 (2009).
T. Bastin, S. Krins, P. Mathonet, M. Godefroid, L. Lamata, and E. Solano, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.103.070503 103, 070503 (2009);
P. Mathonet, S. Krins, M. Godefroid, L. Lamata, E. Solano, and T. Bastin, Phys. Rev. A 1050-2947 10.1103/PhysRevA.81.052315 81, 052315 (2010).
P. Kolenderski and R. Demkowicz-Dobrzanski, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.78.052333 78, 052333 (2008);
P. Kolenderski, e-print arXiv: 0910.3075.
J. Zimba, Electron. J. Theor. Phys. 3, 143 (2006).
S. M. Barnett and P. M. Radmore, Methods in Theoretical Quantum Optics (Oxford University Press, Oxford, 1997).
On completion of this work, we became aware of a similar study in progress, Ref. [11] of D. Markham, e-print arXiv: 1001.0343.
N. J. A. Sloane, R. H. Hardin, W. D. Smith, and others, Tables of Spherical Codes, published electronically at [www.research.att.com/~njas/ packings/].
J. Leech, Math. Gazette PLRAAN 0025-5572 10.2307/3610579 41, 81 (1957).
This website uses cookies to improve user experience. Read more
Save & Close
Accept all
Decline all
Show detailsHide details
Cookie declaration
About cookies
Strictly necessary
Performance
Strictly necessary cookies allow core website functionality such as user login and account management. The website cannot be used properly without strictly necessary cookies.
This cookie is used by Cookie-Script.com service to remember visitor cookie consent preferences. It is necessary for Cookie-Script.com cookie banner to work properly.
Performance cookies are used to see how visitors use the website, eg. analytics cookies. Those cookies cannot be used to directly identify a certain visitor.
Used to store the attribution information, the referrer initially used to visit the website
Cookies are small text files that are placed on your computer by websites that you visit. Websites use cookies to help users navigate efficiently and perform certain functions. Cookies that are required for the website to operate properly are allowed to be set without your permission. All other cookies need to be approved before they can be set in the browser.
You can change your consent to cookie usage at any time on our Privacy Policy page.