Abstract
We theoretically investigate the nonclassicality and entanglement properties of non-Gaussian entangled states generated by using a number-conserving generalized superposition of products (GSP), i.e., \(\left( saa^{\dag }+ta^{\dag }a\right) ^{m}\) with \(s^{2}+t^{2}=1\) on each mode of an input two-mode squeezed coherent (TMSC) state. The simulation results show that, compared to the typical two-mode squeezed vacuum state, the usage of small coherent amplitude is conductive to offering an opportunity for not only effectively enhancing the nonclassicality in terms of antibunching effect and Wigner function, but also significantly improving the entanglement quantified by Einstein–Podolsky–Rosen correlation and Hillery–Zubairy correlation. For the increase of the number of operations, the region of both the existing antibunching effect and the improved entanglement decreases, but this region of the improved teleportation fidelity and the negative distribution of the Wigner function is on the increase. Under an ideal Braunstein and Kimble teleportation protocol, when the generated states are treated as an entangled resource, the optimal teleportation fidelity can be achieved by taking a suitable squeezing parameter and the number of operations for the optimal choices of s. In order to highlight the advantages of the use of the GSP-embedded TMSC, under the same parameters, we also make a comparison about the performances of both the entanglement and the fidelity for different non-Gaussian entangled states, involving the photon-subtracted-then-added TMSC states and the photon-added-then-subtracted TMSC states. It is found that in the regime of small squeezing values, both of the entanglement and the fidelity for the generated states can perform better than the other cases.
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References
Pezze, L., Smerzi, A., Oberthaler, M.K., Schmied, R., Treutlein, P.: Quantum metrology with nonclassical states of atomic ensembles. Rev. Mod. Phys. 90, 035005 (2018)
Ourjoumtsev, A., Jeong, H., Tualle-Brouri, R., Grangier, P.: Generation of optical ‘Schrodinger cats’ from photon number states. Nature 448, 784–786 (2007)
Horodecki, R., Horodecki, P., Horodecki, M., Horodecki, K.: Quantum entanglement. Rev. Mod. Phys. 81, 865 (2009)
Weedbrook, C., Pirandola, S., Garcia-Patron, R., Cerf, N.J., Ralph, T.C., Shapiro, J.H., Lloyd, S.: Gaussian quantum information. Rev. Mod. Phys. 84, 621 (2012)
Braunstein, S.L., Loock, P.V.: Quantum information with continuous variables. Rev. Mod. Phys. 77, 513 (2005)
Osborne, T.J., Nielsen, M.A.: Entanglement, quantum phase transitions, and density matrix renormalization. Quantum Inf. Process. 1, 45–53 (2002)
Karimi, A., Tavassoly, M.K.: Generation of entangled coherent-squeezed states: their entanglement and nonclassical properties. Quantum Inf. Process. 15, 1513–1527 (2016)
Kwon, H., Tan, K.C., Volkoff, T., Jeong, H.: Nonclassicality as a quantifiable resource for quantum metrology. Phys. Rev. Lett. 122, 040503 (2019)
Joo, J., Munro, W.J., Spiller, T.P.: Quantum metrology with entangled coherent states. Phys. Rev. Lett. 107, 083601 (2011)
Gerry, C.C., Campos, R.A.: Generation of maximally entangled states of a Bose–Einstein condensate and Heisenberg-limited phase resolution. Phys. Rev. A 68, 025602 (2003)
Eisert, J., Scheel, S., Plenio, M.B.: Distilling Gaussian states with Gaussian operations is impossible. Phys. Rev. Lett. 89, 137903 (2002)
Yang, Y., Li, F.L.: Entanglement properties of non-Gaussian resources generated via photon subtraction and addition and continuous-variable quantum-teleportation improvement. Phys. Rev. A 80, 022315 (2019)
Marek, P., Jeong, H., Kim, M.S.: Generating “squeezed” superpositions of coherent states using photon addition and subtraction. Phys. Rev. A 78, 063811 (2008)
Navarrete-Benlloch, C., Garcia-Patron, R., Shapiro, J.H., Cerf, N.J.: Enhancing quantum entanglement by photon addition and subtraction. Phys. Rev. A 86, 012328 (2012)
Lee, S.Y., Nha, H.: Quantum state engineering by a coherent superposition of photon subtraction and addition. Phys. Rev. A 82, 053812 (2010)
Hu, L.Y., Xu, X.X., Wang, Z.S., Xu, X.F.: Photon-subtracted squeezed thermal state: nonclassicality and decoherence. Phys. Rev. A 82, 043842 (2010)
Agarwal, G.S., Tara, K.: Nonclassical properties of states generated by the excitations on a coherent state. Phys. Rev. A 43, 492 (1991)
Lee, S.Y., Ji, S.W., Kim, H.J., Nha, H.: Enhancing quantum entanglement for continuous variables by a coherent superposition of photon subtraction and addition. Phys. Rev. A 84, 012302 (2011)
Hu, L.Y., Al-amri, M., Liao, Z.Y., Zubairy, M.S.: Entanglement improvement via a quantum scissor in a realistic environment. Phys. Rev. A 100, 052322 (2019)
Hu, L.Y., Liao, Z.Y., Zubairy, M.S.: Continuous-variable entanglement via multiphoton catalysis. Phys. Rev. A 95, 012310 (2017)
Zhang, H., Ye, W., Xia, Y., Chang, S.K., Wei, C.P., Hu, L.Y.: Improvement of the entanglement properties for entangled states using a superposition of number-conserving operations. Laser Phys. Lett. 16, 085204 (2019)
Liu, C.J., Ye, W., Zhou, W.D., Zhang, H.L., Huang, J.H., Hu, L.Y.: Entanglement of coherent superposition of photon-subtraction squeezed vacuum. Front. Phys. 12, 120307 (2017)
Hu, L.Y., Zhang, Z.M.: Statistical properties of coherent photon-added two-mode squeezed vacuum and its inseparability. J. Opt. Soc. Am. B 30, 518 (2013)
Zhou, W.D., Ye, W., Liu, C.J., Hu, L.Y., Liu, S.Q.: Entanglement improvement of entangled coherent state via multiphoton catalysis. Laser Phys. Lett. 15, 065203 (2018)
Namekata, N., Takahashi, Y., Fujii, G., Fukuda, D., Kurimura, S., Inoue, S.: Non-Gaussian operation based on photon subtraction using a photon-number-resolving detector at a telecommunications wavelength. Nat. Photon. 4, 655–660 (2010)
Zavatta, A., Parigi, V., Bellini, M.: Experimental noncls sicality of single-photon-added thermal light states. Phys. Rev. A 75, 052106 (2007)
Pegg, D.T., Phillips, L.S., Barnett, S.M.: Optical state truncation by projection synthesis. Phys. Rev. Lett. 81, 1604–6 (1998)
Parigi, V., Zavatta, A., Kim, M., Bellini, M.: Probing quantum commutation rules by addition and subtraction of single photons to/from a light field. Science 317, 1890–1893 (2007)
Guo, Y., Ye, W., Zhong, H., Liao, Q.: Continuous-variable quantum key distribution with non-Gaussian quantum catalysis. Phys. Rev. A 99, 032327 (2019)
Ye, W., Zhong, H., Liao, Q., Huang, D., Hu, L.Y., Guo, Y.: Improvement of self-referenced continuous-variable quantum key distribution with quantum photon catalysis. Opt. Express 27, 17186–17198 (2019)
Guo, Y., Liao, Q., Wang, Y.J., Huang, D., Huang, P., Zeng, G.H.: Performance improvement of continuous-variable quantum key distribution with an entangled source in the middle via photon subtraction. Phys. Rev. A 95, 032304 (2017)
Zhang, K.Z., Hu, L.Y., Ye, W., Liu, C.J., Xu, X.X.: Preparation and non-classicality of non-Gaussian quantum states based on catalytic quantum scissors. Laser Phys. Lett. 16, 015204 (2018)
Mehri-Dehnavi, H., Rahimi, R., Email, D., Mohammadzadeh, H., Ebadi, Z., Mirza, B.: Quantum teleportation with nonclassical correlated states in noninertial frames. Quantum Inf. Process. 14, 1025–1034 (2015)
Banik, M., Gazi, M.R.: Classical communication and non-classical fidelity of quantum teleportation. Quantum Inf. Process. 12, 3607–3615 (2013)
Ye, W., Guo, Y., Xia, Y., Zhong, H., Zhang, H., Ding, J.Z., Hu, L.Y.: Discrete modulation continuous-variable quantum key distribution based on quantum catalysis. Acta Phys. Sin. 69, 060301 (2020)
Himadri, S.D., Arpita, C., Rupamanjari, G.: Generating continuous variable entangled states for quantum teleportation using a superposition of number-conserving operations. J. Phys. B: At. Mol. Opt. Phys. 48, 185502 (2015)
Chatterjee, A., Dhar, H.S., Ghosh, R.: Nonclassical properties of states engineered by superpositions of quantum operations on classical states. J. Phys. B: At. Mol. Opt. Phys. 45, 205501 (2012)
Kumar, C., Singh, J., Bose, S., Arvind: Coherence assisted non-Gaussian measurement device independent quantum key distribution. Phys. Rev. A 100, 052329 (2019)
Lee, C.T.: Many-photon anti-bunching in generalized pair coherent states. Phys. Rev. A 41, 1569–1575 (1990)
Fan, H.Y., Zaidi, H.R.: Application of IWOP technique to the generalized Weyl correspondence. Phys. Lett. A 124, 303–307 (1987)
Hillery, M., Zubairy, M.S.: Entanglement conditions for two-mode states: applications. Phys. Rev. A 74, 032333 (2006)
Hillery, M., Zubairy, M.S.: Entanglement conditions for two-mode states. Phys. Rev. Lett. 96, 050503 (2006)
Braunstein, S.L., Kimble, H.J.: Teleportation of continuous quantum variables. Phys. Rev. Lett. 80, 869 (1998)
Marian, P., Marian, T.A.: Continuous-variable teleportation in the characteristic-function description. Phys. Rev. A 74, 042306 (2006)
Hu, L.Y., Liao, Z.Y., Ma, S.L., Zubairy, M.S.: Optimal fdelity of teleportation with continuous variables using three tunable parameters in a realistic environment. Phys. Rev. A 93, 033807 (2016)
Acknowledgements
This work was supported by the National Natural Science Foundation of China (Grant Nos. 61572529, 61821407, 11964013, 11664017), the Training Program for Academic and Technical Leaders of Major Disciplines in Jiangxi Province, the Postgraduate Scientific Research Innovation Project of Hunan Province (Grant No. CX20190126) and the Postgraduate Independent Exploration and Innovation Project of Central South University (Grant No. 2019zzts070).
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Ye, W., Guo, Y., Zhang, H. et al. Nonclassicality and entanglement properties of non-Gaussian entangled states via a superposition of number-conserving operations. Quantum Inf Process 19, 245 (2020). https://doi.org/10.1007/s11128-020-02752-z
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DOI: https://doi.org/10.1007/s11128-020-02752-z