Entropy of entanglement and multifractal exponents for random states

[en] We relate the entropy of entanglement of ensembles of random vectors to their generalized fractal dimensions. Expanding the von Neumann entropy around its maximum we show that the first order only depends on the participation ratio, while higher orders involve other multifractal exponents. These results can be applied to entanglement behavior near the Anderson transition.

Disciplines :

Physics

Author, co-author :

Giraud, O.; Université de Toulouse ; UPS ; Laboratoire de Physique Théorique (IRSAMC) ; F-31062 Toulouse, France ; CNRS ; LPT (IRSAMC) ; F-31062 Toulouse, France

Martin, John ; Université de Liège - ULiège > Département de physique > Physique des atomes froids

Georgeot, B.; Université de Toulouse ; UPS ; Laboratoire de Physique Théorique (IRSAMC) ; F-31062 Toulouse, France ; CNRS ; LPT (IRSAMC) ; F-31062 Toulouse, France

Language :

English

Title :

Entropy of entanglement and multifractal exponents for random states

Publication date :

2009

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

Volume :

Pages :

32308

Peer reviewed :

Peer Reviewed verified by ORBi

Additional URL :

http://link.aps.org/doi/10.1103/PhysRevA.79.032308

Commentary :

http://de.arxiv.org/abs/0807.3716

Available on ORBi :

since 30 November 2009

Statistics

Number of views

80 (13 by ULiège)

Number of downloads

179 (2 by ULiège)

More statistics

Scopus citations^®

Scopus citations^®
without self-citations

OpenCitations

OpenAlex citations

Bibliography

R. Jozsa and N. Linden, Proc. R. Soc. London, Ser. A 459, 2011 (2003). 10.1098/rspa.2002.1097
G. Vidal, Phys. Rev. Lett. 91, 147902 (2003) 10.1103/PhysRevLett.91. 147902
F. Verstraete, D. Porras, and J. I. Cirac, Phys. Rev. Lett. 93, 227205 (2004). 10.1103/PhysRevLett.93.227205
L. Amico, R. Fazio, A. Osterloh, and V. Vedral, Rev. Mod. Phys. 80, 517 (2008). 10.1103/RevModPhys.80.517
G. Vidal, J. I. Latorre, E. Rico, and A. Kitaev, Phys. Rev. Lett. 90, 227902 (2003). 10.1103/PhysRevLett.90.227902
A. D. Mirlin, Phys. Rep. 326, 259 (2000) 10.1016/S0370-1573(99)00091-5
F. Evers and A. D. Mirlin, Rev. Mod. Phys. 80, 1355 (2008). 10.1103/RevModPhys.80.1355
L. Gong and P. Tong, Phys. Rev. E 74, 056103 (2006) 10.1103/PhysRevE.74. 056103
X. Jia, A. R. Subramaniam, I. A. Gruzberg, and S. Chakravarty, Phys. Rev. B 77, 014208 (2008) 10.1103/PhysRevB.77.014208
I. Varga and J. A. Mendez-Bermudez, Phys. Status Solidi C 5, 867 (2008). 10.1002/pssc.200777589
A. A. Pomeransky and D. L. Shepelyansky, Phys. Rev. A 69, 014302 (2004). 10.1103/PhysRevA.69.014302
H.-J. Sommers and K. Zyczkowski, J. Phys. A 37, 8457 (2004) 10.1088/0305-4470/37/35/004
O. Giraud, J. Phys. A 40, 2793 (2007) 10.1088/1751-8113/40/11/014
M. Znidaric, J. Phys. A 40, F105 (2007). 10.1088/1751-8113/40/3/F04
M. L. Mehta, Random Matrices (Academic, New York, 1991).
L. Viola and W. G. Brown, J. Phys. A 40, 8109 (2007) 10.1088/1751-8113/ 40/28/S17
W. G. Brown, L. F. Santos, D. J. Starling, and L. Viola, Phys. Rev. E 77, 021106 (2008). 10.1103/PhysRevE.77.021106
O. Giraud, J. Martin, and B. Georgeot, Phys. Rev. A 76, 042333 (2007). 10.1103/PhysRevA.76.042333
S. Popescu and D. Rohrlich, Phys. Rev. A 56, R3319 (1997). 10.1103/PhysRevA.56.R3319
P. Rungta and C. M. Caves, Phys. Rev. A 67, 012307 (2003). 10.1103/PhysRevA.67.012307
A. J. Scott, Phys. Rev. A 69, 052330 (2004). 10.1103/PhysRevA.69.052330
E. Bogomolny and C. Schmit, Phys. Rev. Lett. 93, 254102 (2004). 10.1103/PhysRevLett.93.254102
J. Martin, O. Giraud, and B. Georgeot, Phys. Rev. E 77, 035201 (R) (2008). 10.1103/PhysRevE.77.035201
B. Georgeot and D. L. Shepelyansky, Phys. Rev. E 62, 3504 (2000) 10.1103/PhysRevE.62.3504
B. Georgeot and D. L. Shepelyansky, Phys. Rev. E 62, 6366 (2000). 10.1103/PhysRevE.62.6366
I. G. Macdonald, Symmetric Functions and Hall Polynomials, 2nd ed. (Oxford University Press, New York, 1995).
D. N. Page, Phys. Rev. Lett. 71, 1291 (1993). 10.1103/PhysRevLett.71.1291