Abstract
We investigate the behavior of quantum correlations in two-coupled double quantum dots (DQDs) with two excess electrons by employing local quantum uncertainty (LQU) and local quantum Fisher information (LQFI) as reliable quantifiers of the amount of quantum correlations contained in the considered physical system. The variations of the quantum correlation measures LQU and LQFI are explored in terms of finite temperature, the weight of the Coulomb coupling between electrons and tunneling coupling between charge qubits. The results show that the Coulomb potential introduces and modulates the nonclassical correlations between both DQDs and that the amount of the quantifiers can be manipulated by changing the tunneling coupling between the two-coupled DQDs. We find that quantum correlations resist low thermal noise and keep a higher value at large values of the Coulomb potential and low temperatures. In addition, our findings confirm that LQFI reveals more nonclassical correlations than LQU in two-coupled DQDs system.
Similar content being viewed by others
Data availability statement
Not applicable.
Code availability
Not applicable.
References
Adesso, G., Bromley, T.R., Cianciaruso, M.: Measures and applications of quantum correlations. J. Phys. A: Math. Theor. 49(47), 473001 (2016)
Austing, D., Honda, T., Muraki, K., Tokura, Y., Tarucha, S.: Quantum dot molecules. Physica B 249, 206–209 (1998)
Benito, M., Mi, X., Taylor, J.M., Petta, J.R., Burkard, G.: Input-output theory for spin-photon coupling in si double quantum dots. Phys. Rev. B 96(23), 235434 (2017)
Bera, M.N.: Role of quantum correlation in metrology beyond standard quantum limit. (2014). arXiv preprint arXiv:1405.5357
Borges, H., Sanz, L., Villas-Bôas, J., Neto, O.D., Alcalde, A.: Tunneling induced transparency and slow light in quantum dot molecules. Phys. Rev. B 85(11), 115425 (2012)
Brennen, G.K.: An observable measure of entanglement for pure states of multi-qubit systems (2003). arXiv preprint quant-ph/0305094
Chapeau-Blondeau, F.: Optimizing qubit phase estimation. Phys. Rev. A 94(2), 022334 (2016)
Chapeau-Blondeau, F.: Entanglement-assisted quantum parameter estimation from a noisy qubit pair: a fisher information analysis. Phys. Lett. A 381(16), 1369–1378 (2017)
Chen, Z.: Wigner–Yanase skew information as tests for quantum entanglement. Phys. Rev. A 71(5), 052302 (2005)
Coffman, V., Kundu, J., Wootters, W.K.: Distributed entanglement. Phys. Rev. A 61(5), 052306 (2000)
Dakić, B., Vedral, V., Brukner, Č: Necessary and sufficient condition for nonzero quantum discord. Phys. Rev. Lett. 105(19), 190502 (2010)
D’Anjou, B., Burkard, G.: Optimal dispersive readout of a spin qubit with a microwave resonator. Phys. Rev. B 100(24), 245427 (2019)
Dillenschneider, R., Lutz, E.: Energetics of quantum correlations. EPL (Europhysics Letters) 88(5), 50003 (2009)
Economou, S.E., Climente, J.I., Badolato, A., Bracker, A.S., Gammon, D., Doty, M.F.: Scalable qubit architecture based on holes in quantum dot molecules. Phys. Rev. B 86(8), 085319 (2012)
Fanchini, F., Castelano, L., Caldeira, A.: Entanglement versus quantum discord in two coupled double quantum dots. New J. Phys. 12(7), 073009 (2010)
Filgueiras, C., Rojas, O., Rojas, M.: Thermal entanglement and correlated coherence in two coupled double quantum dots systems. Ann. Phys. 532(8), 2000207 (2020)
Ganczarek, W., Kuś, M., Życzkowski, K.: Barycentric measure of quantum entanglement. Phys. Rev. A 85(3), 032314 (2012)
Genoni, M.G., Olivares, S., Paris, M.G.: Optical phase estimation in the presence of phase diffusion. Phys. Rev. Lett. 106(15), 153603 (2011)
Giovannetti, V., Lloyd, S., Maccone, L.: Quantum-enhanced measurements: beating the standard quantum limit. Science 306(5700), 1330–1336 (2004)
Girolami, D., Tufarelli, T., Adesso, G.: Characterizing nonclassical correlations via local quantum uncertainty. Phys. Rev. Lett. 110(24), 240402 (2013)
Gorman, J., Hasko, D., Williams, D.: Charge-qubit operation of an isolated double quantum dot. Phys. Rev. Lett. 95(9), 090502 (2005)
Guo, J.-L., Wei, J.-L., Qin, W., Mu, Q.-X.: Examining quantum correlations in the xy spin chain by local quantum uncertainty. Quantum Inf. Process. 14(4), 1429–1442 (2015)
Haddadi, S., Bohloul, M.: A brief overview of bipartite and multipartite entanglement measures. Int. J. Theor. Phys. 57(12), 3912–3916 (2018)
Haddadi, S., Pourkarimi, M.R., Akhound, A., Ghominejad, M.: Thermal quantum correlations in a two-dimensional spin star model. Mod. Phys. Lett. A 34(22), 1950175 (2019)
Haseli, S., Haddadi, S., Pourkarimi, M.R.: Probing the entropic uncertainty bound and quantum correlations in a quantum dot system. Laser Phys. 31(5), 055203 (2021)
Hassan, A.S.M., Lari, B., Joag, P.S.: Tight lower bound to the geometric measure of quantum discord. Phys. Rev. A 85(2), 024302 (2012)
Helstrom, C.W.: Quantum detection and estimation theory. J. Stat. Phys. 1(2), 231–252 (1969)
Henderson, L., Vedral, V.: Classical, quantum and total correlations. J. Phys. A: Math. Gen. 34(35), 6899 (2001)
Horodecki, M., Oppenheim, J.: (quantumness in the context of) resource theories. Int. J. Mod. Phys. B 27(01n03), 1345019 (2013)
Hu, M.-L., Hu, X., Wang, J., Peng, Y., Zhang, Y.-R., Fan, H.: Quantum coherence and geometric quantum discord. Phys. Rep. 762, 1–100 (2018)
Huelga, S.F., Macchiavello, C., Pellizzari, T., Ekert, A.K., Plenio, M.B., Cirac, J.I.: Improvement of frequency standards with quantum entanglement. Phys. Rev. Lett. 79(20), 3865–3868 (1997)
Itakura, T., Tokura, Y.: Dephasing due to background charge fluctuations. Phys. Rev. B 67(19), 195320 (2003)
Karpat, G., Çakmak, B., Fanchini, F.: Quantum coherence and uncertainty in the anisotropic xy chain. Phys. Rev. B 90(10), 104431 (2014)
Kay, S.M.: Fundamentals of Statistical Signal Processing: Estimation Theory. Prentice-Hall, Inc (1993)
Khedif, Y., Haddadi, S., Pourkarimi, M.R., Daoud, M.: Thermal correlations and entropic uncertainty in a two-spin system under dm and ksea interactions. Mod. Phys. Lett. A 36(29), 2150209 (2021)
Kim, S., Li, L., Kumar, A., Wu, J.: Characterizing nonclassical correlations via local quantum fisher information. Phys. Rev. A 97, 032326 (2018)
Loss, D., DiVincenzo, D.P.: Quantum computation with quantum dots. Phys. Rev. A 57(1), 120 (1998)
Luo, S.: Wigner-Yanase skew information and uncertainty relations. Phys. Rev. Lett. 91(18), 180403 (2003)
Luo, S.: Wigner-Yanase skew information vs. quantum fisher information. Proc. Am. Math. Soc. 132(3), 885–890 (2004)
Luo, S., Fu, S.: Geometric measure of quantum discord. Phys. Rev. A 82(3), 034302 (2010)
Mansour, M., Dahbi, Z.: Quantum secret sharing protocol using maximally entangled multi-qudit states. Int. J. Theor. Phys. 59(12), 3876–3887 (2020)
Mansour, M., Dahbi, Z., Essakhi, M., Salah, A.: Quantum correlations through spin coherent states. Int. J. Theor. Phys. 60(6), 2156–2174 (2021)
Mansour, M., Daoud, M.: Entangled thermal mixed states for multi-qubit systems. Mod. Phys. Lett. B 33(22), 1950254 (2019)
Mansour, M., Daoud, M., Dahbi, Z.: Randomized entangled mixed states from phase states. Int. J. Theor. Phys. 59(3), 895–907 (2020)
Mansour, M., Haddadi, S.: Bipartite entanglement of decohered mixed states generated from maximally entangled cluster states. Mod. Phys. Lett. A 36(03), 2150010 (2021)
Mansour, M., Hassouni, Y.: Entanglement of spin coherent mixed states. Int. J. Quantum Inf. 14(01), 1650004 (2016)
Mansour, M., Oulouda, Y., Sbiri, A., El Falaki, M.: Decay of negativity of randomized multiqubit mixed states. Laser Phys. 31(3), 035201 (2021)
Meyer, D.A., Wallach, N.R.: Global entanglement in multiparticle systems. J. Math. Phys. 43(9), 4273–4278 (2002)
Mintert, F., Kuś, M., Buchleitner, A.: Concurrence of mixed bipartite quantum states in arbitrary dimensions. Phys. Rev. Lett. 92(16), 167902 (2004)
Nielsen, M.A., Chuang, I.: Quantum Computation and Quantum Information (2002)
Oliveira, P., Sanz, L.: Bell states and entanglement dynamics on two coupled quantum molecules. Ann. Phys. 356, 244–254 (2015)
Ollivier, H., Zurek, W.H.: Quantum discord: a measure of the quantumness of correlations. Phys. Rev. Lett. 88(1), 017901 (2001)
Paris, M.G.: Quantum estimation for quantum technology. Int. J. Quantum Inf. 7(supp01), 125–137 (2009)
Paula, F., de Oliveira, T.R., Sarandy, M.: Geometric quantum discord through the schatten 1-norm. Phys. Rev. A 87(6), 064101 (2013)
Qin, X.-K.: Decoherence of the hybrid qubit in a double quantum dot. EPL (Europhysics Letters) 114(3), 37006 (2016)
Renou, M.-O., Wang, Y., Boreiri, S., Beigi, S., Gisin, N., Brunner, N.: Limits on correlations in networks for quantum and no-signaling resources. Phys. Rev. Lett. 123(7), 070403 (2019)
Sbiri, A., Mansour, M., Oulouda, Y.: Local quantum uncertainty versus negativity through gisin states. Int. J. Quantum Inf. 19(05), 2150023 (2021)
Scott, A.J.: Multipartite entanglement, quantum-error-correcting codes, and entangling power of quantum evolutions. Phys. Rev. A 69(5), 052330 (2004)
Shinkai, G., Hayashi, T., Ota, T., Fujisawa, T.: Correlated coherent oscillations in coupled semiconductor charge qubits. Phys. Rev. Lett. 103, 056802 (2009)
Slaoui, A., Daoud, M., Laamara, R.A.: The dynamics of local quantum uncertainty and trace distance discord for two-qubit x states under decoherence: a comparative study. Quantum Inf. Process. 17(7), 1–24 (2018)
Souza, F., Oliveira, P., Sanz, L.: Quantum entanglement driven by electron-vibrational mode coupling. Phys. Rev. A 100(4), 042309 (2019)
Streltsov, A.: Quantum correlations beyond entanglement. In: Quantum Correlations Beyond Entanglement, pp. 17–22. Springer (2015)
Szafran, B.: Paired electron motion in interacting chains of quantum dots. Phys. Rev. B 101(7), 075306 (2020)
Urdampilleta, M., Chatterjee, A., Lo, C.C., Kobayashi, T., Mansir, J., Barraud, S., Betz, A.C., Rogge, S., Gonzalez-Zalba, M.F., Morton, J.J.: Charge dynamics and spin blockade in a hybrid double quantum dot in silicon. Phys. Rev. X 5(3), 031024 (2015)
Villas-Bôas, J., Govorov, A., Ulloa, S.E.: Coherent control of tunneling in a quantum dot molecule. Phys. Rev. B 69(12), 125342 (2004)
Wigner, E. P., Yanase, M. M.: Information contents of distributions. In: Part I: Particles and Fields. Part II: Foundations of Quantum Mechanics, pp. 452–460. Springer (1997)
Yang, C., Guo, Y.-N., Peng, H.-P., Lu, Y.-B.: Dynamics of local quantum uncertainty for a two-qubit system under dephasing noise. Laser Phys. 30(1), 015203 (2019)
Ye, B.-L., Li, B., Wang, Z.-X., Li-Jost, X., Fei, S.-M.: Quantum fisher information and coherence in one-dimensional xy spin models with Dzyaloshinsky–Moriya interactions. Sci. China Phys. Mech. Astron. 61(11), 1–7 (2018)
Funding
Not applicable.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no conflict of interest.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Elghaayda, S., Dahbi, Z. & Mansour, M. Local quantum uncertainty and local quantum Fisher information in two-coupled double quantum dots. Opt Quant Electron 54, 419 (2022). https://doi.org/10.1007/s11082-022-03829-y
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s11082-022-03829-y