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.
Similar content being viewed by others
References
Einstein, A., Podolsky, B., Rosen, N.: Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. 47, 777 (1935)
Schrödinger, E.: Die gegenwärtige situation in der quantenmechanik. Die Naturwissenschaften 23, 807 (1935)
Bell, J.S.: On the Einstein–Podolsky–Rosen paradox. Physics 1, 195 (1964)
Bennett, C.H., DiVincenzo, D.P.: Quantum information and computation. Nature 404, 247 (2000)
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)
Maleki, Y., Maleki, A.: Entangled multimode spin coherent states of trapped ions. J. Opt. Soc. Am. B 35, 1211–1217 (2018)
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)
Dür, W., Vidal, G., Cirac, J.I.: Three qubits can be entangled in two inequivalent ways. Phys. Rev. A 62, 062314 (2000)
Horodecki, R., Horodecki, P., Horodecki, M., Horodecki, K.: Quantum entanglement. Rev. Mod. Phys. 81, 865 (2009)
Greenberger, D.M., Horne, M.A., Shimony, A., Zeilinger, A.: Bell’s theorem without inequalities. Am. J. Phys. 58, 1131 (1990)
Sharma, A., Hawrylak, P.: Greenberger–Horne–Zeilinger states in a quantum dot molecule. Phys. Rev. B 83, 125311 (2011)
Hiltunen, T., Harju, A.: Maximal tripartite entanglement between singlet–triplet qubits in quantum dots. Phys. Rev. B 89, 115322 (2014)
Loss, D., DiVincenzo, D.P.: Quantum computation with quantum dots. Phys. Rev. A 57, 120 (1998)
Burkard, G., Loss, D., DiVincenzo, D.P.: Coupled quantum dots as quantum gates. Phys. Rev. B 59, 2070 (1999)
DiVincenzo, D.P., Bacon, D., Kempe, J., Burkard, G., Whaley, K.B.: Universal quantum computation with the exchange interaction. Nature 408, 339–342 (2000)
Scarola, V.W., Park, K., Das Sarma, S.: Chirality in quantum computation with spin cluster qubits. Phys. Rev. Lett. 93, 120503 (2004)
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)
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)
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)
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)
Fu, J.-H., Zhang, G.-F.: Effect of three-spin interaction on thermal entanglement in Heisenberg XXZ model. Quantum Inf. Process 16, 275 (2017)
Yang, J., Huang, Y.: Tripartite and bipartite quantum correlations in the XXZ spin chain with three-site interaction. Quantum Inf. Process 16, 281 (2017)
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)
Pachos, J.K., Plenio, M.B.: Three-spin interactions in optical lattices and criticality in cluster Hamiltonians. Phys. Rev. Lett. 93, 056402 (2004)
Pachos, J.K., Rico, E.: Effective three-body interactions in triangular optical lattices. Phys. Rev. A 70, 053620 (2004)
Bermudez, A., Porras, D., Martin-Delgado, M.A.: Competing many-body interactions in systems of trapped ions. Phys. Rev. A 79, 060303(R) (2009)
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)
Nielsen, M.A.: Quantum information theory, Ph.D. thesis, The University of New Mexico, USA (1998), quant-ph/0011036
Arnesen, M.C., Bose, S., Vedral, V.: Natural thermal and magnetic entanglement in the 1D Heisenberg model. Phys. Rev. Lett. 87, 017901 (2001)
Wang, X.G., Fu, H., Solomon, A.I.: Thermal entanglement in three-qubit Heisenberg models. J. Phys. A: Math. Gen. 34, 11307 (2001)
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)
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)
Sabin, C., García-Alcaine, G.: A classification of entanglement in three-qubit systems. Eur. Phys. J. D 48, 435 (2008)
Vidal, G., Werner, R.F.: Computable measure of entanglement. Phys. Rev. A 65, 032314 (2002)
Hill, S., Wootters, W.K.: Entanglement of a pair of quantum bits. Phys. Rev. Lett. 78, 5022 (1997)
Wootters, W.K.: Entanglement of formation of an arbitrary state of two qubits. Phys. Rev. Lett. 80, 2245 (1998)
Coffman, V., Kundu, J., Wootters, W.K.: Distributed entanglement. Phys. Rev. A 61, 052306 (2000)
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)
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)
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)
Gühne, O., Toth, G.: Entanglement detection. Phys. Rep. 474, 1 (2009)
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)
Acknowledgements
We thank Aleksandra Dimić and Nikola Paunković for fruitful discussions. This research is funded by the Serbian Ministry of Science (Project ON171035).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Milivojević, M. Maximal thermal entanglement using three-spin interactions. Quantum Inf Process 18, 48 (2019). https://doi.org/10.1007/s11128-018-2163-8
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s11128-018-2163-8