Abstract
The current work shows the efficacy of Dzyaloshinshkii–Moriya interaction to free the bound entanglement. Based on the work (Sharma et al. in Quant. Info. Proc. 15:1539 2016), we present further results in two qutrits bound entangled state proposed by Jurkowski et al. We consider a closed system of two qutrits and an auxiliary qutrit which interacts with either one of the two qutrits in a closed system. We erase the auxiliary qutrit from the system by doing partial trace operation and open system dynamics has been studied. We have found, the probability amplitude of auxiliary qutrit does not affect the system, while DM interaction plays a major role to govern the dynamics. The realignment and CCNR criteria have been used to detect the bound entanglement in the state, while for quantification of entanglement the negativity has been used. We explored the dynamics with all the possible cases of Jurkowski et al. bound entangled state.
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Einstein, A., Podolsky, B., Rosen, N.: Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. Lett. 47, 777 (1935)
Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, UK (2000)
Sharma, K.K., Gerdt, V.P., Gerdt, P.V.: Milestone Developments in Quantum Information and No-Go Theorems, Lecture Notes in Computer Science book series (LNCS, volume 12563) (2021)
Bennett, C.H., Brassard, G., Crépeau, C., Jozsa, R., Peres, A., Wootters, W.K.: Teleporting an unknown quantum state via dual classical and einstein-podolsky-rosen channels. Phys. Rev. Lett. 70, 1895 (1993)
Ekert, A.K.: Quantum cryptography based on bell’s theorem. Phys. Rev. Lett. 67, 661 (1991)
Meyer, D.A.: Quantum strategies. Phys. Rev. Lett. 82, 1052 (1999)
Lugiato, L., Gatti, A., Brambilla, E.: Quantum imaging. J. Opt. B Quantum Semiclass. Opt. 4, 176 (2002)
Horodecki, M., Horodecki, P., Horodecki, R.: Mixed-state entanglement and distillation: is there a bound entanglement in nature? Phys. Rev. Lett. 80, 5239 (1998)
Horodecki, P., Horodecki, R.: Distillation and bound entanglement. Quant. Info. Comp. 1, 45 (2001)
Horodecki, P., Horodecki, M., Horodecki, R.: Bound entanglement can be activated. Phys. Rev. Lett. 82, 1056 (1999)
Dür, W., Cirac, J.I.: Activating bound entanglement in multiparticle systems. Phys. Rev. A. 62, 022302 (2000)
Kaneda, F., Shimizu, R., Ishizaka, S., Mitsumori, Y., Kosaka, H., Edamatsu, K.: Experimental activation of bound entanglement. Phys. Rev. Lett. 109, 040501 (2012)
Amselem, E., Bourennane, M.: Experimental four-qubit bound entanglement. Nat. Phys. 5, 748 (2009)
Lavoie, J., Kaltenbaek, R., Piani, M., Resch, K.J.: Experimental bound entanglement in a four-photon state. Phys. Rev. Lett. 105, 130501 (2010)
Amselem, E., Sadiq, M., Bourennane, M.: Experimental bound entanglement through a pauli channel. Sci. Rep. 3, 1966 (2013)
Peres, A.: Quantum Theory: Concepts and Methods. Kluwer Academic Publishers, Netherlands (1995)
Peres, A.: Higher order Schmidt decompositions. Phys. Lett. A 202, 16 (1995)
Schmidt, E.: Zur theorie der linearen und nichtlinearen integralgleichungen. Math. Ann. 63, 433 (1907)
Ekert, A., Knight, P.L.: Entangled quantum systems and the Schmidt decomposition. Am. J. Phys. 63, 415 (1995)
Horodecki, M., Horodecki, P., Horodecki, R.: Separability of mixed states: necessary and sufficient conditions. Phys. Lett. A 223, 1 (1996)
Vidal, G., Werner, R.F.: Computable measure of entanglement. Phys. Rev. A 65, 032314 (2002)
Plenio, M.B., Virmani, S.: An introduction to entanglement measures. Quant. Inf. Comp. 7, 1 (2007)
Peres, A.: Separability criterion for density matrices. Phys. Rev. Lett. 77, 1413 (1996)
Horodecki, P.: Separability criterion and inseparable mixed states with positive partial transposition. Phys. Lett. A. 232, 333 (1997)
Horodecki, M.: Entanglement measures. Quant. Info. Comp. 1, 3 (2001)
Chen, K., Wu, L.: A matrix realignment method for recognizing entanglement. Quant. Info. Comp. 3(3), 193 (2003)
Rudolph, O.: Further results on the cross norm criterion for separability. Quant. Inf. Proc. 4, 219 (2005)
Zhang, C., Zhang, Y., Zhang, S., Guo, G.: Entanglement detection beyond the computable cross-norm or realignment criterion. Phys. Rev. A. 77, 060301(R) (2008)
Dzyaloshinsky, I.: A thermodynamic theory of weak ferromagnetism of antiferromagnetics. J. Phys. Chem. Solids 4, 241 (1958)
Moriya, T.: New mechanism of anisotropic superexchange interaction. Phys. Rev. Lett. 4, 228 (1960)
Moriya, T.: Anisotropic superexchange interaction and weak ferromagnetism. Phys. Rev. 120, 91 (1960)
Qiang, Z., Xiao-Ping, Z., Qi-Jun, Z., Zhong-Zhou, R.: Entanglement dynamics of a Heisenberg chain with Dzyaloshinskii-Moriya interaction. Chin. Phys. B 18, 3210 (2009)
Qiang, Z., Ping, S., Xiao-Ping, Z., Zhong-Zhou, R.: Control of entanglement sudden death induced by Dzyaloshinskii-Moriya interaction. Chin. Phys. C 34, 1583 (2010)
Qiang, Z., Qi-Jun, Z., Xiao-Ping, Z., Zhong-Zhou, R.: Controllable entanglement sudden birth of Heisenberg spins. Chin. Phys. C 35, 135 (2011)
Sharma, K.K., Awasth, S.K., Pandey, S.N.: Entanglement sudden death and birth in qubit-qutrit systems under Dzyaloshinskii-Moriya interaction. Quantum Inf. Process. 12, 3437 (2013)
Sharma, K.K., Pandey, S.N.: Entanglement dynamics in two parameter Qubit-Qutrit states under Dzyaloshinskii-Moriya interaction. Quantum Inf. Process. 13, 2017 (2014)
Sharma, K.K., Pandey, S.N.: Influence of Dzyaloshinshkii-Moriya interaction on quantum correlations in two-qubit werner states and MEMS. Quantum Inf. Process. 14, 1361 (2015)
Sharma, K.K., Pandey, S.N.: Dynamics of entanglement in Qubit-Qutrit with X-component of DM interaction. Commun. Theor. Phys. 65, 278 (2016)
Sharma, K.K., Pandey, S.N.: Robustness of Greenberger-Horne-Zeilinger and W states against Dzyaloshinskii-Moriya interaction. Quantum Inf. Process. 15, 4995 (2016)
Sharma, K.K., Pandey, S.N.: Dzyaloshinskii-Moriya interaction as an agent to free the bound entangled states. Quantum Inf. Process. 15, 1539 (2016)
Bruss, D., Macchiavello, C.: Optimal eavesdropping in cryptography with three-dimensional quantum states. Phys. Rev. Lett. 88, 127901 (2002)
Cerf, N.J., Bourennane, M., Karlsson, A., Gisin, N.: Security of quantum key distribution using d-level systems. Phys. Rev. Lett. 88, 127902 (2002)
Oberst, H.: Resonance fluorescence of single Barium ions, diplomarbeit. Innsbruck University (1999)
Guo-Qiang, Z., Xiao-Guang, W.: Quantum dynamics of bound entangled states. Commun. Theor. Phys. 49, 343 (2008)
Song, W., Chen, L., Zhu, S.: Sudden death of distillability in qutrit-qutrit systems. Phys. Rev. A 80, 012331 (2009)
Ali, M.: Distillability sudden death in qutrit-qutrit systems under global and multilocal dephasing. Phys. Rev. A 81, 042303 (2010)
Ali, M.: Distillability sudden death in qutrit-qutrit systems under amplitude damping. J. Phys. B At. Mol. Opt. Phys. 43, 045504 (2010)
Khan, S., Khan, M.K.: Nondistillability of distillable qutrit-qutrit states under depolarising noise. J. Mod. Opt. 58, 918 (2011)
Xiao-San, M., Ming-Fan, R., Guang-Xing, Z., An-Min, W.: Dynamics of entanglement of Qutrit-Qutrit states with stochastic dephasing. Commun. Theor. Phys. 56, 258 (2011)
Jiang, H., Mao-Fa, F., Bai-Yuan, Y., Xiang, L.: Distillability sudden death in a two qutrit systems under a thermal reservoir. Chin. Phys. B. 21, 084205 (2012)
Sharma, K.K., Sinha, S.: Trade-off between squashed entanglement and concurrence in bipartite quantum states. Int. J. Theor. Phys. 60, 3651 (2021)
Jurkowski, J., Chruscinski, D., Rutkowski, A.: A class of bound entangled states of two qutrits. Open Syst. Inf. Dyn. 16, 235 (2009)
Klimov, A.B., Guzmán, R., Retamal, J.C., Saavedra, C.: Qutrit quantum computer with trapped ions. Phys. Rev. A 67, 062313 (2003)
Hugh, D Mc.: Trapped-ion qutrit spin molecule quantum computer. New J. Phys. 7, 174 (2005)
Horodecki, M., Horodecki, P.: Reduction criterion of separability and limits for a class of distillation protocols. Phys. Rev. A 59, 4206 (1999)
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Sharma, K.K., Sinha, S. & Chandra, K. Efficacy of Moriya interaction to free the bound entangled state. Quantum Inf Process 21, 21 (2022). https://doi.org/10.1007/s11128-021-03383-8
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DOI: https://doi.org/10.1007/s11128-021-03383-8