Abstract
We review recent works that relate entanglement of random vectors to their localization properties. In particular, the linear entropy is related by a simple expression to the inverse participation ratio, while next orders of the entropy of entanglement contain information about e.g. the multifractal exponents. Numerical simulations show that these results can account for the entanglement present in wavefunctions of physical systems.
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References
Amico L., Fazio R., Osterloh A. and Vedral V.: 2008. Rev. Mod. Phys., 80, 517
Bennett C.H., Hayden P., Leung D., Shor P. and Winter A.: 2005. IEEE Trans. Inf. Theory, 51, 56
Bogomolny E. and Schmit C.: 2004. Phys. Rev. Lett., 93, 254102
Brennen G.K.: 2003. Quant. Inf. Comp., 3, 619
Brown W.G., Santos L.F., Starling D.J. and Viola L.: 2008. Phys. Rev. E, 77, 021106
Cappellaro P., Emerson J., Boulant N., Ramanathan C. and Cory D.G.: 2005. Phys. Rev. Lett., 94, 020502
Emerson J., Weinstein Y.S., Saraceno M., Lloyd S. and Cory D.S.: 2003. Science, 302, 2098
Evers F. and Mirlin A.D.:2007. arXiv:0707.4378
Facchi P., Marzolino U., Parisi G., Pascazio S. and Scardicchio A.: 2008. Phys. Rev. Lett., 101, 050502
Georgeot B. and Shepelyansky D.L.: 2000a. Phys. Rev. E, 62, 3504
Georgeot B. and Shepelyansky D.L.: 2000b Phys. Rev. E 62, 6366
Giannoni M.-J., Voros A. and Zinn-Justin J. (Eds.): 1991 Proceedings of the 52th Les Houches Summer School, North-Holland, Amsterdam
Giraud O.: 2007a. J. Phys. A, 40, 2793
Giraud O.: 2007b. J. Phys. A, 40, F1043
Giraud O., Marklof J. and O'Keefe S.: 2004. J. Phys. A., 37, L303
Giraud O., Georgeot B. and Shepelyansky D.L.: 2005. Phys. Rev. E, 72, 036203
Giraud O., Martin J. and Georgeot B.: 2007. Phys. Rev. A, 76, 042333
Giraud O., Martin J. and Georgeot B.: 2009. Phys. Rev. A, 79, 032308
Harrow A., Hayden P. and Leung D.: 2004. Phys. Rev. Lett., 92, 187901
Hayden P., Leung D., Shor P. and Winter A.: 2004. Commun. Math. Phys., 250, 317
Jozsa R. and Linden N.: 2003. Proc. R. Soc. London Ser. A, 459, 2011
Lubkin E.: 1978. J. Math. Phys., 19, 1028
Martin J., Giraud O. and Georgeot B.: 2008. Phys. Rev. E, 77, R035201
Mejia-Monasterio C., Benenti G., Carlo G.G. and Casati G.: 2005. Phys. Rev. A, 71, 062324
Meyer A.D. and Wallach N.R.: 2002. J. Math. Phys., 43, 4273
Mirlin A.D.: 2000. Phys. Rep., 326, 259
Nielsen M.A. and Chuang I.L.: 2000, Quantum computation and quantum information. Cambridge University Press, Cambridge
Page D.N.: 1993. Phys. Rev. Lett., 71, 1291
Pomeransky A.A. and Shepelyansky D.L.: 2004. Phys. Rev. A, 69, 014302
Popescu S. and Rohrlich D.: 1997. Phys. Rev. A, 56, R3319
Rungta P. and Caves C.M.: 2003. Phys. Rev. A, 67, 012307
Scott A.J.: 2004. Phys. Rev. A, 69, 052330
Sommers H.-J. and Zyczkowski K.: 2004. J. Phys. A, 37, 8457
Verstraete F., Porras D. and Cirac J.I.: 2004. Phys. Rev. Lett., 93, 227205
Vidal G.: 2003. Phys. Rev. Lett., 91, 147902
Viola L. and Brown W.G.: 2007. J. Math. Phys., 43, 8109
Weinstein Y.S. and Hellberg C.S.: 2005. Phys. Rev. Lett., 95, 030501
Znidaric M.: 2007. J. Phys. A, 40, F105
Znidaric M., Prosen T., Benenti G. and Casati G.: 2007. J. Phys. A, 40, 13787
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Giraud, O., Georgeot, B., Martin, J. (2009). Entanglement and Localization of Wavefunctions. In: Casati, G., Matrasulov, D. (eds) Complex Phenomena in Nanoscale Systems. NATO Science for Peace and Security Series B: Physics and Biophysics. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-3120-4_5
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DOI: https://doi.org/10.1007/978-90-481-3120-4_5
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-3118-1
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