Abstract
We systematically study the unextendible maximally entangled basis in arbitrary bipartite spaces \(\mathbb {C}^{d} \otimes \mathbb {C}^{d^{\prime }}\ (d<d^{\prime })\). We give an example of UMEB in \(\mathbb {C}^{2} \otimes \mathbb {C}^{5}\), and show that there are q d 2-member UMEBs in \(\mathbb {C}^{d} \otimes \mathbb {C}^{d^{\prime }}(d^{\prime }=qd+r, \ q,r\in \mathbb {Z}^{+}, r<d)\). Moreover, we present two complete UMEBs in \(\mathbb {C}^{3} \otimes \mathbb {C}^{4}\) which are mutually unbiased.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bennett, C.H., Divincenzo, D.P., Mor, T., Shor, P.W., Smolin, J.A., Terhal, B.M.: Phys. Rev. Lett. 82, 5385 (1999)
Bennett, C.H., DiVincenzo, D.P., Fuchs, C.A., Mor, T., Rains, E., Shor, P.W., Smolin, J.A., Wootters, W.K.: Phys. Rev. A 59, 1070–1091 (1999)
DiVincenzo, D.P., Mor, T., Shor, P.W., Smolin, J.A., Terhal, B.M.: Commun. Math. Phys. 238, 379–410 (2003)
Terhal, B.M.: Linear Algebra Appl. 323, 61–73 (2001)
Bravyi, S., Smolin, J.A.: Phys. Rev. A 84, 042306 (2011)
Barreiro, J.T., Wei, T.C., Kwiat, P.G.: Nat. Phys. 4, 282 (2008)
Ishizaka, S., Hiroshima, T.: Phys. Rev. A 79, 042306 (2009)
Albeverio, S., Fei, S.M., Yang, W.L.: Phys. Rev. A 66, 012301 (2002)
Li, Z.G., Zhao, M.J., Fei, S.M., Fan, H., Liu, W.M.: Quantum Inf. Comput. 63, 12 (2012)
Chen, B., Fei, S.M.: Phys. Rev. A 88, 034301 (2013)
Wootters, W.K., Fields, B.D.: Ann. Phys. 191, 363–381 (1989)
Vourdas, A.: Rep. Prog. Phys. 67 (3), 267–320 (2004)
Bjork, G., Klimov, A.B., Sanchez-Soto, L.L.: Prog. Opt. 51, 469–516 (2008)
Nikolopoulos, G.M., Alber, G.: Phys. Rev. A 72, 032320 (2005)
Mafu, M., Dudley, A., Goyal, S., Giovannini, D., McLaren, M., Padgett, M.J., Konrad, T., Petruccione, F., Lutkenhaus, N., Forbes, A.: Phys. Rev. A 88, 032305 (2013)
Paw lowski, M., Zukowski, M.: Phys. Rev. A 81, 042326 (2010)
Paz, J.P., Roncaglia, A. J., Saraceno, M.: Phys. Rev. A 72, 012309 (2005)
Revzen, M.: J. Phys. A 46, 075303 (2013)
Boykin, P.O., Sitharm, M., Tiep, P.H., Wocjan, P.: Quantum Inf. Comp. 7, 371 (2007)
Lay, D.C.: Linear algebra and it’s applications. Pearson Education (2002)
Acknowledgments
This research was supported by Natural Science Foundation of China(11361065);the Natural Science Foundation of Jilin Province(201215239);Yanbian University Research Found (2013, No.17)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Nan, H., Tao, YH., Li, LS. et al. Unextendible Maximally Entangled Bases and Mutually Unbiased Bases in ℂd ⊗ ℂd′ . Int J Theor Phys 54, 927–932 (2015). https://doi.org/10.1007/s10773-014-2288-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10773-014-2288-1