Abstract
An operational representation of concurrence measuring the entanglement of bipartite systems by means of averages of basic observables is discussed. We prove the validity of this representation for bipartite systems with any dimension of a single-party Hilbert space. We show that Wigner-Yanase “skew” information gives a reasonable estimation of the amount of entanglement (in ebits) carried by mixed two-qubit states
Similar content being viewed by others
References
G. Vidal, J. Mod. Opt., 47, 355 (2000).
W. Dur, G. Vidal, and J. I. Cirac, Phys. Rev. A, 62, 06231 (2000).
F. Verstraete, J. Dehaene, and B. De Moor, Phys. Rev. A, 68, 012103 (2003).
A. A. Klyachko and A. S. Shumovsky, J. Opt. B: Quantum Semiclass. Opt., 5, S322 (2003).
A. A. Klyachko, E-print quant-ph/0206012.
A. A. Klyachko and A. S. Shumovsky, J. Opt. B: Quantum Semiclass. Opt., 6, S29 (2004).
A. A. Klyachko and A. S. Shumovsky, E-print quant-ph/0512213; J. Phys. Conf. Ser., 36, 87 (2006).
E. Vinberg and V. Popov, Invariant Theory, Springer, Berlin (1992).
S. Hill and W. K. Wootters, Phys. Rev. Lett., 78, 5022 (1997). W. K. Wooters, Phys. Rev. Lett. 80, 2245 (1998).
V. Coffman, J. Kundu, and W. K. Wootters, Phys. Rev. A, 61, 052306 (2000).
A. Miyake, Phys. Rev. A, 67, 012108 (2003).
P. Rungta, V. Bužek, C. M. Caves, M. Hillery, and G. J. Milburn, Phys. Rev. A, 64, 042315 (2001).
F. Minnert, M. Kuś, and A. Buchleitner, Phys. Rev. Lett., 92, 167902 (2004).
F. Verstraete, M. A. Martin-Delgado, and J. I. Cirac, Phys. Rev. Lett. 92, 087201 (2004).
B.-Q. Jin and V. E. Korepin, Phys. Rev. A, 69, 062314 (2004).
A. A. Klyachko, B. Oztop, and A. S. Shumovsky, Appl. Phys. Lett., 88, 124102 (2006).
J. S. Bell, Rev. Mod. Phys., 38, 447 (1966).
E. P Wigner, Z. Phys., 131, 101 (1952). E. P. Wigner and M. M. Yanase, Proc. Natl. Acad. Sci. USA, 19, 910 (1963).
J. von Neumann, Mathematical Foundations of Quantum Mechanics, Princeton University Press, Princeton (1996).
R. Hermann, Lie Groups for Physicists, Benjamin, New York (1966).
G. G. Emch, Mathematical and Conceptual Foundations of 20th Century Physics, North Holland, Amsterdam (1984).
C. M. Caves and G. J. Milburn, Opt. Commun., 179, 439 (2000).
A. T. Bölükbaşi and T. Dereli, E-print quant-ph/0511111; J. Phys. Conf. Ser., 36, 28 (2006).
H. Bechman-Pasquinucci and A. Peres, Phys. Rev. Lett., 85, 3313 (2000). D. Bruss and C. Macchiavello, Phys. Rev. Lett., 88, 127901 (2002). G. A. Maslennikov, A. A. Zhukov, M. V. Chekhova, and S. P. Kulik, J. Opt. B: Quantum Semicalss. Opt., 5, 530 (2003). D. Kaszlikowski, D. K. L. Oi, M. Christandl, K. Chang, A. Ekert, L. C. Kwek, and C. H. Oh, Phys. Rev. A, 67, 012310 (2003). T. Durt T., N. Cerf, N. Gisin, and M. Zukowski, Phys. Rev. A, 67, 012311 (2003). T. Durt, D. Kaszlikowski, J.-L. Chen, and L. C. Kwek, Phys. Rev. A, 69, 032313 (2004).
M. A. Can, A. A. Klyachko, and A. S. Shumovsky, J. Opt. B: Quantum Semiclass. Opt., 7, L1 (2005).
M. A. Can, A. A. Klyachko, and A. S. Shumovsky, Phys. Rev. A, 66, 02111 (2002).
M. Nielsen and I. Chuang, Quantum Computation and Quantum Information, Cambridge University Press, New York (2000).
D. Bruß, J. Math. Phys., 43, 4237 (2002).
A. Cabello, Phys. Rev. A, 65, 032108 (2002).
A. A. Klyachko, E-print quant-ph/0511102; J. Phys. Conf. Ser., 36, 72 (2006).
A. Binicioglu, Ö. Çakir, A. A. Klyachko, and A. S. Shumovsky, Int. J. Quantum Inform., 3, 661 (2005).
L. D. Landau and E. M. Lifshitz, Statistical Physics, Pergamon Press, Oxford (1959).
H. Araki and M. M. Yanase, Phys. Rev., 120, 622 (1960). F. J. Dyson and A. Leonard, J. Math. Phys., 8, 423 (1967). F. J. Dyson, J. Math. Phys., 8, 1538 (1967). E. H. Lieb and M. B. Ruskai, Phys. Rev. Lett., 30, 434 (1973). A. Uhlman, Comm. Math. Phys., 54, 21 (1977). M. Ozawa, Phys. Rev. Lett., 88, 050402 (2002). J. Řeháček and Z. Hradil, Phys. Rev. Lett., 90 127904 (2003). S.-L. Luo, Phys. Rev. Lett., 91, 180403 (2003). P. Gibilisco and T. Isola, J. Math. Phys., 44, 3752 (2003). S.-L. Luo and Q. Zhang, Phys. Rev. A, 69, 032106 (2004).
V. B. Berestetskii, E. M. Lifshitz, and L. P. Pitaevskii, Quantum Electrodynamics, Pergamon Press, Oxford (1982).
A. V. Burlakov, M. V. Chekhova, O. A. Karabutova, D. N. Klyshko, and S. P. Kulik, Phys. Rev. A, 60, R4209 (1999). M. B. Nasr, A. F. Abouraddy, M. C. Booth, B. E. A. Saleh, A. V. Sergienko, M. C. Teich, U. Kempe, and R. Wollescheensky, Phys. Rev. A, 65, 023816 (2002). G. DiGiuseppe, M. Atature, M. Shaw, A. V. Sergienko, B. E. A. Saleh, M. C. Teich, A. J. Miller, S. W. Nam, and J. M. Martinis, Phys. Rev. A, 68, 063817 (2003). Yu. I. Bogdanov, M. V. Chekhova, S. P. Kulik, G. A. Maslennikov, A. A. Zhukov, C. H. Oh, and M. K. Tey, Phys. Rev. Lett., 93, 230503 (2004).
A. L. Onishchik and E. B. Vinberg (eds.), Lie Groups and Lie Algebras III, Encyclopedia of Math. Science, Springer, Berlin (1994), Vol. 41.
R. F. Werner, Phys. Rev. A, 40, 4277 (1989).
T. Hiroshima and S. Ishizaka, Phys. Rev. A, 62, 044302 (2000).
M. Murano, M. B. Plenio, S. Popesku, V. Vedral, and P. L. Knight, Phys. Rev. A, 57, R4075, R4078 (1998).
V. A. Andreev and V. I. Man’ko, J. Opt. B: Quantum Semiclass. Opt., 2 122 (2000). O. V. Man’ko, V. I. Man’ko, G. Marmo, A. Shaji, E. C. G. Sudarshan, and F. Zaccaria, Phys. Lett. A, 339, 194 (2005).
Author information
Authors and Affiliations
Additional information
Dedicated to the memory of Andrey Vinogradov.
Manuscript submitted by the authors in English on April 12, 2006.
Rights and permissions
About this article
Cite this article
Klyachko, A.A., Öztop, B. & Shumovsky, A.S. Entanglement and its operational measure. J Russ Laser Res 27, 389–402 (2006). https://doi.org/10.1007/s10946-006-0021-0
Issue Date:
DOI: https://doi.org/10.1007/s10946-006-0021-0