Advertisement

Maximal thermal entanglement using three-spin interactions

  • Marko MilivojevićEmail author
Article
  • 27 Downloads

Abstract

Three-spin interactions in three-qubit systems at thermal equilibrium can be used for simple and efficient creation of maximally entangled states. We do not require set of gates to achieve this goal; rather, maximal thermal entanglement naturally arises by appropriately tuning the interactions present in the system. Within the broad range of parameter regimes found, we identify the ones accessible in triple quantum dot and triangular optical lattice, thus opening a way toward simple implementation of maximally entangled states with different types of three-spin interactions. Our results suggest tight connection between the presence of W type of entanglement and magnetization, enabling experimental detection of the W state.

Keywords

Quantum entanglement GHZ and W state Three-spin interaction 

Notes

Acknowledgements

We thank Aleksandra Dimić and Nikola Paunković for fruitful discussions. This research is funded by the Serbian Ministry of Science (Project ON171035).

References

  1. 1.
    Einstein, A., Podolsky, B., Rosen, N.: Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. 47, 777 (1935)ADSCrossRefGoogle Scholar
  2. 2.
    Schrödinger, E.: Die gegenwärtige situation in der quantenmechanik. Die Naturwissenschaften 23, 807 (1935)ADSCrossRefGoogle Scholar
  3. 3.
    Bell, J.S.: On the Einstein–Podolsky–Rosen paradox. Physics 1, 195 (1964)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Bennett, C.H., DiVincenzo, D.P.: Quantum information and computation. Nature 404, 247 (2000)ADSCrossRefGoogle Scholar
  5. 5.
    Röthlisberger, B., Lehmann, J., Saraga, D.S., Traber, P., Loss, D.: Highly entangled ground states in tripartite qubit systems. Phys. Rev. Lett. 100, 100502 (2008)ADSCrossRefGoogle Scholar
  6. 6.
    Maleki, Y., Maleki, A.: Entangled multimode spin coherent states of trapped ions. J. Opt. Soc. Am. B 35, 1211–1217 (2018)ADSCrossRefGoogle Scholar
  7. 7.
    Maleki, Y., Zheltikov, A.M.: Generating maximally-path-entangled number states in two spin ensembles coupled to a superconducting flux qubit. Phys. Rev. A 97, 012312 (2018)ADSCrossRefGoogle Scholar
  8. 8.
    Dür, W., Vidal, G., Cirac, J.I.: Three qubits can be entangled in two inequivalent ways. Phys. Rev. A 62, 062314 (2000)ADSMathSciNetCrossRefGoogle Scholar
  9. 9.
    Horodecki, R., Horodecki, P., Horodecki, M., Horodecki, K.: Quantum entanglement. Rev. Mod. Phys. 81, 865 (2009)ADSMathSciNetCrossRefGoogle Scholar
  10. 10.
    Greenberger, D.M., Horne, M.A., Shimony, A., Zeilinger, A.: Bell’s theorem without inequalities. Am. J. Phys. 58, 1131 (1990)ADSMathSciNetCrossRefGoogle Scholar
  11. 11.
    Sharma, A., Hawrylak, P.: Greenberger–Horne–Zeilinger states in a quantum dot molecule. Phys. Rev. B 83, 125311 (2011)ADSCrossRefGoogle Scholar
  12. 12.
    Hiltunen, T., Harju, A.: Maximal tripartite entanglement between singlet–triplet qubits in quantum dots. Phys. Rev. B 89, 115322 (2014)ADSCrossRefGoogle Scholar
  13. 13.
    Loss, D., DiVincenzo, D.P.: Quantum computation with quantum dots. Phys. Rev. A 57, 120 (1998)ADSCrossRefGoogle Scholar
  14. 14.
    Burkard, G., Loss, D., DiVincenzo, D.P.: Coupled quantum dots as quantum gates. Phys. Rev. B 59, 2070 (1999)ADSCrossRefGoogle Scholar
  15. 15.
    DiVincenzo, D.P., Bacon, D., Kempe, J., Burkard, G., Whaley, K.B.: Universal quantum computation with the exchange interaction. Nature 408, 339–342 (2000)ADSCrossRefGoogle Scholar
  16. 16.
    Scarola, V.W., Park, K., Das Sarma, S.: Chirality in quantum computation with spin cluster qubits. Phys. Rev. Lett. 93, 120503 (2004)ADSCrossRefGoogle Scholar
  17. 17.
    Hsieh, C.-Y., Rene, A., Hawrylak, P.: Herzberg circuit and Berry’s phase in chirality-based coded qubit in a triangular triple quantum dot. Phys. Rev. B 86, 115312 (2012)ADSCrossRefGoogle Scholar
  18. 18.
    Hsieh, C.-Y., Shim, Y.-P., Korkusinski, M., Hawrylak, P.: Physics of lateral triple quantum-dot molecules with controlled electron numbers. Rep. Prog. Phys. 75, 114501 (2012)CrossRefGoogle Scholar
  19. 19.
    Milivojević, M., Stepanenko, D.: Effective spin Hamiltonian of a gated triple quantum dot in the presence of spin-orbit interaction. J. Phys: Condens. Matter 29, 405302 (2017)Google Scholar
  20. 20.
    Han, J.-X., Hu, Y., Jin, Y., Zhang, G.-F.: Influence of intrinsic decoherence on tripartite entanglement and bipartite fidelity of polar molecules in pendular states. J. Chem. Phys. 144, 134308 (2016)ADSCrossRefGoogle Scholar
  21. 21.
    Fu, J.-H., Zhang, G.-F.: Effect of three-spin interaction on thermal entanglement in Heisenberg XXZ model. Quantum Inf. Process 16, 275 (2017)ADSMathSciNetCrossRefGoogle Scholar
  22. 22.
    Yang, J., Huang, Y.: Tripartite and bipartite quantum correlations in the XXZ spin chain with three-site interaction. Quantum Inf. Process 16, 281 (2017)CrossRefGoogle Scholar
  23. 23.
    Tseng, C.H., Somaroo, S., Sharf, Y., Knill, E., Laflamme, R., Havel, T.F., Cory, D.G.: Quantum simulation of a three-body-interaction Hamiltonian on an NMR quantum computer. Phys. Rev. A 61, 012302 (1999)ADSCrossRefGoogle Scholar
  24. 24.
    Pachos, J.K., Plenio, M.B.: Three-spin interactions in optical lattices and criticality in cluster Hamiltonians. Phys. Rev. Lett. 93, 056402 (2004)ADSCrossRefGoogle Scholar
  25. 25.
    Pachos, J.K., Rico, E.: Effective three-body interactions in triangular optical lattices. Phys. Rev. A 70, 053620 (2004)ADSCrossRefGoogle Scholar
  26. 26.
    Bermudez, A., Porras, D., Martin-Delgado, M.A.: Competing many-body interactions in systems of trapped ions. Phys. Rev. A 79, 060303(R) (2009)ADSCrossRefGoogle Scholar
  27. 27.
    Capogrosso-Sansone, B., Wessel, S., Büchler, H.P., Zoller, P., Pupillo, G.: Phase diagram of one-dimensional hard-core bosons with three-body interactions. Phys. Rev. B 79, 020503(R) (2009)ADSCrossRefGoogle Scholar
  28. 28.
    Nielsen, M.A.: Quantum information theory, Ph.D. thesis, The University of New Mexico, USA (1998), quant-ph/0011036Google Scholar
  29. 29.
    Arnesen, M.C., Bose, S., Vedral, V.: Natural thermal and magnetic entanglement in the 1D Heisenberg model. Phys. Rev. Lett. 87, 017901 (2001)ADSCrossRefGoogle Scholar
  30. 30.
    Wang, X.G., Fu, H., Solomon, A.I.: Thermal entanglement in three-qubit Heisenberg models. J. Phys. A: Math. Gen. 34, 11307 (2001)ADSMathSciNetCrossRefGoogle Scholar
  31. 31.
    Zhang, G.-F.: Thermal entanglement and teleportation in a two-qubit Heisenberg chain with Dzyaloshinskii–Moriya anisotropic antisymmetric interaction. Phys. Rev. A 75, 034304 (2007)ADSCrossRefGoogle Scholar
  32. 32.
    Wang, J.-B., Zhang, G.-F.: Thermal entanglement between atoms in the four-cavity linear chain coupled by single-mode fibers. Int. J. Theor. Phys. 57, 2585 (2018)CrossRefGoogle Scholar
  33. 33.
    Sabin, C., García-Alcaine, G.: A classification of entanglement in three-qubit systems. Eur. Phys. J. D 48, 435 (2008)ADSMathSciNetCrossRefGoogle Scholar
  34. 34.
    Vidal, G., Werner, R.F.: Computable measure of entanglement. Phys. Rev. A 65, 032314 (2002)ADSCrossRefGoogle Scholar
  35. 35.
    Hill, S., Wootters, W.K.: Entanglement of a pair of quantum bits. Phys. Rev. Lett. 78, 5022 (1997)ADSCrossRefGoogle Scholar
  36. 36.
    Wootters, W.K.: Entanglement of formation of an arbitrary state of two qubits. Phys. Rev. Lett. 80, 2245 (1998)ADSCrossRefGoogle Scholar
  37. 37.
    Coffman, V., Kundu, J., Wootters, W.K.: Distributed entanglement. Phys. Rev. A 61, 052306 (2000)ADSCrossRefGoogle Scholar
  38. 38.
    Maleki, Y., Khashami, F., Mousavi, Y.: Entanglement of three-spin states in the context of SU(2) coherent states. Int. J. Theor. Phys. 54, 210 (2015)CrossRefGoogle Scholar
  39. 39.
    Yildirim, T., Harris, A.B., Aharony, A., Entin-Wohlman, O.: Anisotropic spin Hamiltonians due to spin-orbit and Coulomb exchange interactions. Phys. Rev. B 52, 10239 (1995)ADSCrossRefGoogle Scholar
  40. 40.
    Milivojević, M.: Symmetric spin-orbit interaction in triple quantum dot and minimisation of spin-orbit leakage in CNOT gate. J. Phys.: Condens. Matter 30, 085302 (2018)ADSGoogle Scholar
  41. 41.
    Gühne, O., Toth, G.: Entanglement detection. Phys. Rep. 474, 1 (2009)ADSMathSciNetCrossRefGoogle Scholar
  42. 42.
    Maleki, Y., Zheltikov, A.M.: Witnessing quantum entanglement in ensembles of nitrogen–vacancy centers coupled to a superconducting resonator. Opt. Exp. 26, 17849–17858 (2018)ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.NanoLab, QTP Center, Faculty of PhysicsUniversity of BelgradeBelgradeSerbia

Personalised recommendations