Abstract
We investigate entangled states of an atomic trapped ion interacting with two phonons in the Λ configuration forming a twelve-dimensional Hilbert space. We study two elaborated measures, namely, the concurrence C and negativity N, which are important in current theoretical studies. Therefore, we work with the three-dimensional reduced density matrix in calculating the measures elaborated for pure qudit states in the ionic–phononic system. To demonstrate the benefits of the family of the two measures elaborated, we perform the calculations for different values of the Lamb–Dicke (LD) parameter η = 0.01, 0.3, and 0.5. Finally, we show that the pure qudit states under study are maximum entangled states.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
A. Einstein, B. Podolsky, N. Rosen, Phys. Rev., 47, 777 (1935).
E. Schrödinger, Proc. Cambridge Philos. Soc., 31, 555 (1935).
R. Blatt and D. Wineland, Nature, 453, 1008 (2008).
P. Maunz, D. L. Moehring, S. Olmschenk, et al., Nature Phys., 3, 538 (2007).
C. P. Yang, Q. P. Su, and S. Han, Phys. Rev. A, 86, 022329 (2012).
Y. A. Lee and G. Vidal, Phys. Rev. A, 88, 042318 (2013).
J. S. Kim, A. Das, and B. C. Sanders, Phys. Rev. A, 79, 012329 (2009).
R. Dermez and Ö. E. Müstecaplıoğlu, Phys. Scr., 71, 015304 (2009).
R. Dermez and S. Özen, Eur. Phys. J. D., 57, 431 (2010).
R. Dermez and S. Özen, Phys. Scr., 85, 055009 (2012).
R. Dermez and S. A. Khalek, J. Russ. Laser Res., 32, 287 (2011).
S. Özen and R. Dermez, Balkan Phys. Lett., 16, 161046 (2009).
R. Dermez, B. Deveci, and D. Ö. Güney, Eur. Phys. J. D., 67, 120 (2013).
W. K. Wootters, Phys. Rev. Lett., 80, 2245 (1998).
G. Vidal and R. F. Werner, Phys. Rev. A, 65, 032314 (2002).
Ö. E. Müstecaplıoğlu, Phys. Rev. A, 68, 023811 (2003).
Z.-J. Wang and F. Chen, Chin. Phys. Lett., 24, 1570 (2007).
R. Dermez, J. Russ. Laser Res., 37, 572 (2016).
R. Dermez, J. Phys.: Conf. Ser., 766, 012012 (2016).
R. Dermez, J. Russ. Laser Res., 34, 192 (2013).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Dermez, R. Concurrence and Negativity as a Family of Two Measures Elaborated for Pure Qudit States. J Russ Laser Res 38, 408–415 (2017). https://doi.org/10.1007/s10946-017-9661-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10946-017-9661-5