Pilukuli Janardhana Geetha,   Sudha^*, Alevoor Raghavendra Usha Devi

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Department of Physics, Kuvempu University, Shankaraghatta, Shimoga, India.
1Department of Physics, Kuvempu University, Shankaraghatta, Shimoga, India 2Inspire Institute Inc., Alexandria, USA.
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Abstract: We examine here the proposition that all multiparty quantum states can be made monogamous by considering positive integral powers of any quantum correlation measure. With Rajagopal-Rendell quantum deficit as the measure of quantum correlations for symmetric 3-qubit pure states, we illustrate that monogamy inequality is satisfied for higher powers of quantum deficit. We discuss the drawbacks of this inequality in quantification of correlations in the state. We also prove a monogamy inequality in higher powers of classical mutual information and bring out the fact that such inequality needs not necessarily imply restricted shareability of correlations. We thus disprove the utility of higher powers of any correlation measure in establishing monogamous nature in multiparty quantum states.

Keywords: Mutual Information, Sharing of Classical and Quantum Correlations, Monogamy of Quantum Correlations

Cite this paper: Geetha, P. , Sudha, &. and Devi, A. (2014) What Does Monogamy in Higher Powers of a Correlation Measure Mean?. Journal of Modern Physics, 5, 1294-1301. doi: 10.4236/jmp.2014.514130.

References

[1]   Coffman. V., Kundu. J. and Wootters, W.K. (2000) Physical Review A, 61, Article ID: 052306.
http://dx.doi.org/10.1103/PhysRevA.61.052306

[2]   Osborne, T.J. and Verstraete, F. (2006) Physical Review Letters, 96, Article ID: 220503.
http://dx.doi.org/10.1103/PhysRevLett.96.220503

[3]   Koashi, M. and Winter, A. (2004) Physical Review A, 69, Article ID: 022309.
http://dx.doi.org/10.1103/PhysRevA.69.022309

[4]   Yang, D. (2006) Physics Letters A, 360, 249-250.
http://dx.doi.org/10.1016/j.physleta.2006.08.027

[5]   Ou, Y.-C. and Fan, H. (2007) Physical Review A, 75, Article ID: 062308.
http://dx.doi.org/10.1103/PhysRevA.75.062308

[6]   Yu, C.-S. and Song, H.-S. (2008) Physical Review A, 77, Article ID: 032329.
http://dx.doi.org/10.1103/PhysRevA.77.032329

[7]   Kim. J.S., Das, A. and Sanders, B.C. (2009) Physical Review A, 79, Article ID: 012329.
http://dx.doi.org/10.1103/PhysRevA.79.012329

[8]   Lee, S. and Park, J. (2009) Physical Review A, 79, Article ID: 054309.
http://dx.doi.org/10.1103/PhysRevA.79.054309

[9]   de Oliveira, T.R. (2009) Physical Review A, 80, Article ID: 022331.
http://dx.doi.org/10.1103/PhysRevA.80.022331

[10]   Cornelio, M.F. and de Oliveira, M.C. (2010) Physical Review A, 81, Article ID: 032332.
http://dx.doi.org/10.1103/PhysRevA.81.032332

[11]   Kim, J.S. and Sanders, B.C. (2011) Journal of Physics A: Mathematical and Theoretical, 44, Article ID: 295303.
http://dx.doi.org/10.1088/1751-8113/44/29/295303

[12]   Zhao, M.J., Fei, S.M. and Wang, Z.X. (2010) International Journal of Quantum Information, 8, 905.
http://dx.doi.org/10.1142/S0219749910006216

[13]   Seevinck, M.P. (2010) Quantum Information Processing, 9, 273-294.
http://dx.doi.org/10.1007/s11128-009-0161-6

[14]   Giorgi, G.L. (2011) Physical Review A, 84, Article ID: 054301.
http://dx.doi.org/10.1103/PhysRevA.84.054301

[15]   Fanchini, F.F., de Oliveira, M.C., Castelano, L.K. and Cornelio, M.F. (2013) Physical Review A, 87, Article ID: 032317.
http://dx.doi.org/10.1103/PhysRevA.87.032317

[16]   Prabhu, R., Pati, A.K., Sen De, A. and Sen, U. (2012) Physical Review A, 85, Article ID: 040102(R).
http://dx.doi.org/10.1103/PhysRevA.85.040102

[17]   Sudha, Usha Devi, A.R. and Rajagopal, A.K. (2012) Physical Review A, 85, Article ID: 012103.
http://dx.doi.org/10.1103/PhysRevA.85.012103

[18]   Ren, X.J. and Fan, H. (2013) Quantum Information & Computation, 13, 469-478.
http://arxiv.org/abs/1111.5163

[19]   Liu, S.Y., Zhang, Y.R., Zhao, L.M., Yang, W.L. and Fan, H. (2013) Annals of Physics, 348, 256. arXiv:1307.4848v2.
http://arxiv.org/abs/1307.4848v2

[20]   Liu, S.Y., Li, B., Yang, W.L. and Fan, H. (2013) Physical Review A, 87, Article ID: 062120.
http://dx.doi.org/10.1103/PhysRevA.87.062120

[21]   Streltsov, A., Adesso, G., Piani, M. and Bruss, D. (2012) Physical Review Letters, 109, Article ID: 050503.
http://dx.doi.org/10.1103/PhysRevLett.109.050503

[22]   Bai, Y.K., Zhang, N., Ye, M.Y. and Wang, Z.D. (2013) Physical Review A, 88, Article ID: 012123.
http://dx.doi.org/10.1103/PhysRevA.88.012123

[23]   Salini, K., Prabhu, R., Sen De, A. and Sen, U. (2012) Annals of Physics, 348, 297. arXiv: 1206.4029.
http://arxiv.org/abs/1206.4029

[24]   Ollivier, H. and Zurek, W.H. (2002) Physical Review Letters, 88, Article ID: 017901.
http://dx.doi.org/10.1103/PhysRevLett.88.017901

[25]   Rajagopal, A.K. and Rendell, R.W. (2002) Physical Review A, 66, Article ID: 022104.
http://dx.doi.org/10.1103/PhysRevA.66.022104

[26]   Majorana, E. (1932) Il Nuovo Cimento, 9, 43-50.
http://dx.doi.org/10.1007/BF02960953

[27]   Bastin, T., Krins, S., Mathonet, P., Godefroid, M., Lamata, L. and Solano, E. (2009) Physical Review Letters, 103, Article ID: 070503.
http://dx.doi.org/10.1103/PhysRevLett.103.070503

[28]   Usha Devi, A.R., Sudha and Rajagopal, A.K. (2012) Quantum Information Processing, 11, 685.

[29]   Nielsen, M.A. and Chuang, I.L. (2002) Quantum Computation and Quantum Information. Cambridge University Press, Cambridge.