Research Paper: The Entanglement of Three-mode Spin Coherent States

Document Type : Research Paper

Authors

1 Researcher, Supreme National Defense University, Tehran

2 Assistant Professor, Supreme National Defense University, Tehran, Iran.

Abstract

In this study, the detection method of entanglement of 3-mode spin coherence states is investigated. For this purpose, by properly defining the computational codes, these states are mapped to a three qubit quantum state, and then, by using the Mermin- Kalyshko inequality, the entanglement of these states is studied and an analytical relationship to determine the entanglement region is presented. The results of numerical analysis of the extracted inequality show that the entanglement region of these states depends on the coherence parameters, the amount of spin as well as the phase of the states. For example, in the case where the values of the coherence parameters are equal but with opposite signs, by adjusting the coherence phase, the degree of entanglement can be controlled such that the maximum entanglement occurs . More important, as the value of spin increases, the allowable range of the coherence parameter for entanglement detection increases. These results are consistent with the data reported in the study of the degree of entanglement of 2-mode superposition of spin coherent states using other measures and criteria of entanglement.  The findings of this study can be used in the study of non-classical and quantum systems and quantum correlations in quantum information science.

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References

[1]         Kurzyk D., Introduction to Quantum Entanglement, Vol. 24 (2012).
[2]         Duarte F. J., Fundamentals of Quantum Entanglement (IOP Publishing Bristol, 2019).
[3]         Schrödinger E., Die Gegenwärtige Situation in Der Quantenmechanik, Naturwissenschaften 23, 823 (1935).
[4]         Formaggio J. A., Kaiser D. I., Murskyj M. M., and Weiss T. E., Violation of the Leggett-Garg Inequality in Neutrino Oscillations, Phys. Rev. Lett. 117, 50402 (2016).
[5]         Hensen B., Bernien H., Dréau A. E., Reiserer A., Kalb N., Blok M. S., Ruitenberg J., Vermeulen R. F. L., Schouten R. N., Abellán C., Amaya W., Pruneri V., Mitchell M. W., Markham M., Twitchen D. J., Elkouss D., Wehner S., Taminiau T. H., and Hanson R., Nature 526, 682 (2015).
[6]         Maleki Y. and Ahansaz B., Quantum Correlations in Qutrit-like Superposition of Spin Coherent States, Laser Phys. Lett. 16, 75205 (2019).
[7]         Wang X. and Sanders B. C., Phys. Rev. A 65, 12303 (2001).
[8]         K. Berrada, S. A. Khalek, and C. H. R. Ooi, Quantum Metrology with Entangled Spin-Coherent States of Two Modes, Phys. Rev. A 86, 33823 (2012).
[9]         Maleki Y. and Maleki A., Entangled Multimode Spin Coherent States of Trapped Ions, J. Opt. Soc. Am. B 35, 1211 (2018).
[10]       Chryssomalakos C., Guzmán-González E., and Serrano-Ensástiga E., Geometry of Spin Coherent States, J. Phys. A Math. Theor. 51, 165202 (2018).
[11]       Maleki Y., Khashami F., and Mousavi Y., Entanglement of Three-Spin States in the Context of SU(2) Coherent States, Int. J. Theor. Phys. 54, 210 (2015).
[12]       Fu H., Wang X., and Solomon A. I., Maximal Entanglement of Nonorthogonal States: Classification, Phys. Lett. A 291, 73 (2001).
[13]       Maleki Y., Entanglement and Decoherence in Two-Dimensional Coherent State Superpositions, Int. J. Theor. Phys. 56, 757 (2017).
[14]       Mansour M., Dahbi Z., Essakhi M., and Salah A., Quantum Correlations Through Spin Coherent States, Int. J. Theor. Phys. 60, 2156 (2021).
[15]       Wang X., Sanders B. C., and Pan S., Entangled Coherent States for Systems WithSU(2) AndSU(1,1) Symmetries, J. Phys. A. Math. Gen. 33, 7451 (2000).
[16]       Mansour M. and Dahbi Z., Entanglement of Bipartite Partly Non-Orthogonal 1/2-Spin Coherent States, Laser Phys. 30, 85201 (2020).
[17]       Maleki Y., Generation and Entanglement of Multi-Dimensional Multi-Mode Coherent Fields in Cavity QED, Quantum Inf. Process. 15, 4537 (2016).
[18]       Maleki Y. and Zheltikov A. M., Linear Entropy of Multiqutrit Nonorthogonal States, Opt. Express 27, 8291 (2019).
[19]       Walther P., Aspelmeyer M., Resch K. J., and Zeilinger A., Experimental Violation of a Cluster State Bell Inequality, Phys. Rev. Lett. 95, 20403 (2005).
[20]       Larsson J., Loopholes in Bell Inequality Tests of Local Realism, J. Phys. A Math. Theor. 47, 424003 (2014).
[21]       Gottesman D., Theory of Quantum Secret Sharing, Phys. Rev. A 61, 42311 (2000).
[22]       Gazeau J.-P., Coherent States in Quantum Physics (Wiley, 2009).
[23]       Radcliffe J. M., Some Properties of Coherent Spin States, J. Phys. A Gen. Phys. 4, 313 (1971).
[24]       Klyshko D. N., The Bell and GHZ Theorems: A Possible Three-Photon Interference Experiment and the Question of Nonlocality, Phys. Lett. A 172, 399 (1993).
[25]       Mermin N. D., Extreme Quantum Entanglement in a Superposition of Macroscopically Distinct States, Phys. Rev. Lett. 65, 1838 (1990).
[26]       Seevinck M. and Uffink J., Sufficient Conditions for Three-Particle Entanglement and Their Tests in Recent Experiments, Phys. Rev. A 65, 12107 (2001).
[27]       Dür W., Multipartite Bound Entangled States That Violate Bell’s Inequality, Phys. Rev. Lett. 87, 230402 (2001).

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History

  • Receive Date: 01 July 2021
  • Revise Date: 16 November 2021
  • Accept Date: 16 December 2021

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