Abstract
We assess the performance of an entanglement indicator which can be obtained directly from tomograms, avoiding state reconstruction procedures. In earlier work, we have examined this tomographic entanglement indicator, and a variant obtained from it, in the context of continuous variable systems. It has been shown that, in multipartite systems of radiation fields, these indicators fare as well as standard measures of entanglement. In this paper we assess these indicators in the case of two generic hybrid quantum systems, the double Jaynes–Cummings model and the double Tavis–Cummings model using, for purposes of comparison, the quantum mutual information as a standard reference for both quantum correlations and entanglement. The dynamics of entanglement is investigated in both models over a sufficiently long time interval. We establish that the tomographic indicator provides a good estimate of the extent of entanglement both in the atomic subsystems and in the field subsystems. An indicator obtained from the tomographic indicator as an approximation, however, does not capture the entanglement properties of atomic subsystems, although it is useful for field subsystems. Our results are inferred from numerical calculations based on the two models, simulations of relevant equivalent circuits in both cases, and experiments performed on the IBM computing platform.
Similar content being viewed by others
References
Yu, T., Eberly, J.: Sudden death of entanglement. Science 323, 598 (2009)
Man, Z.X., Xia, Y.J., An, N.B.: Entanglement dynamics for the double Tavis–Cummings model. Eur. Phys. J. D. 53, 229 (2009)
Vogel, W., Filho, RLdM: Nonlinear Jaynes–Cummings dynamics of a trapped ion. Phys. Rev. A 52, 4214 (1995)
Deppe, F., Mariantoni, M., Menzel, E., Marx, A., Saito, S., Kakuyanagi, K., Tanaka, H., Meno, T., Semba, K., Takayanagi, H., et al.: Two-photon probe of the Jaynes–Cummings model and controlled symmetry breaking in circuit QED. Nat. Phys. 4, 686 (2008)
Retzker, A., Solano, E., Reznik, B.: Tavis–Cummings model and collective multiqubit entanglement in trapped ions. Phys. Rev. A 75, 022312 (2007)
Laha, P., Sudarsan, B., Lakshmibala, S., Balakrishnan, V.: Entanglement dynamics in a model tripartite quantum system. Int. J. Theor. Phys. 55, 4044 (2016)
Laha, P., Lakshmibala, S., Balakrishnan, V.: Nonclassical effects in optomechanics: dynamics and collapse of entanglement. J. Opt. Soc. Am. B 36, 575 (2019)
Li, X., Shang, J., Ng, H.K., Englert, B.G.: Optimal error intervals for properties of the quantum state. Phys. Rev. A 94, 062112 (2016)
Rohith, M., Sudheesh, C.: Signatures of entanglement in an optical tomogram. J. Opt. Soc. Am. B 33, 126 (2016)
Sharmila, B., Saumitran, K., Lakshmibala, S., Balakrishnan, V.: Signatures of nonclassical effects in optical tomograms. J. Phys. B: At. Mol. Opt. 50, 045501 (2017)
Sharmila, B., Lakshmibala, S., Balakrishnan, V.: Estimation of entanglement in bipartite systems directly from tomograms. Quantum Inf. Process. 18, 236 (2019)
Wang, Y., Li, Y., Yin, Zq, Zeng, B.: 16-qubit IBM universal quantum computer can be fully entangled. NPJ Quantum Inf. 4, 46 (2018)
Mooney, G.J., Hill, C.D., Hollenberg, L.C.: Entanglement in a 20-qubit superconducting quantum computer. Sci. Rep. 9, 13465 (2019)
Behera, B.K., Seth, S., Das, A., Panigrahi, P.K.: Demonstration of entanglement purification and swapping protocol to design quantum repeater in IBM quantum computer. Quantum Inf. Process. 18(4), 108 (2019)
Satyajit, S., Srinivasan, K., Behera, B.K., Panigrahi, P.K.: Nondestructive discrimination of a new family of highly entangled states in IBM quantum computer. Quantum Inf. Process. 17(9), 212 (2018)
Deffner, S.: Demonstration of entanglement assisted invariance on IBM’s quantum experience. Heliyon 3(11), e00444 (2017)
Lamata, L., Parra-Rodriguez, A., Sanz, M., Solano, E.: Digital-analog quantum simulations with superconducting circuits. Adv. Phys. X 3, 1457981 (2018)
IBM Q: Documentation and support. https://quantum-computing.ibm.com/support
Qiskit: An Open-Source Framework for Quantum Computing. https://qiskit.org
Vogel, K., Risken, H.: Determination of quasiprobability distributions in terms of probability distributions for the rotated quadrature phase. Phys. Rev. A 40, 2847 (1989)
Ibort, A., Man’ko, V.I., Marmo, G., Simoni, A., Ventriglia, F.: An introduction to the tomographic picture of quantum mechanics. Phys. Scr. 79, 065013 (2009)
Lvovsky, A.I., Raymer, M.G.: Continuous-variable optical quantum-state tomography. Rev. Mod. Phys. 81, 299 (2009)
Thew, R.T., Nemoto, K., White, A.G., Munro, W.J.: Qudit quantum-state tomography. Phys. Rev. A 66, 012303 (2002)
Acknowledgements
We acknowledge the use of the IBM Q for this work. The views expressed are those of the authors and do not reflect the official policy or position of IBM or the IBM Q team. We have also used the Department Computing Facility, Department of Physics, IIT Madras.
Author information
Authors and Affiliations
Corresponding author
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
Sharmila, B., Lakshmibala, S. & Balakrishnan, V. Tomographic entanglement indicators in multipartite systems. Quantum Inf Process 19, 127 (2020). https://doi.org/10.1007/s11128-020-02625-5
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s11128-020-02625-5