Abstract
We study the degree of entanglement of arbitrary superpositions of m, n photon-added coherent states (PACS) \(\mathinner {|{\psi }\rangle } \propto u \mathinner {|{{\alpha },m}\rangle }\mathinner {|{{\beta },n }\rangle }+ v \mathinner {|{{\beta },n}\rangle }\mathinner {|{{\alpha },m}\rangle }\) using the concurrence and obtain the general conditions for maximal entanglement. We show that photon addition process can be identified as an entanglement enhancer operation for superpositions of coherent states (SCS). Specifically for the known bipartite positive SCS: \(\mathinner {|{\psi }\rangle } \propto \mathinner {|{\alpha }\rangle }_a\mathinner {|{-\alpha }\rangle }_b + \mathinner {|{-\alpha }\rangle }_a\mathinner {|{\alpha }\rangle }_b \) whose entanglement tends to zero for \(\alpha \rightarrow 0\), can be maximal if al least one photon is added in a subsystem. A full family of maximally entangled PACS is also presented. We also analyzed the decoherence effects in the entangled PACS induced by a simple depolarizing channel . We find that robustness against depolarization is increased by adding photons to the coherent states of the superposition. We obtain the dependence of the critical depolarization \(p_{\text {crit}}\) for null entanglement as a function of \(m,n, \alpha \) and \(\beta \).
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Jozsa, R., Linden, N.: On the role of entanglement in quantum-computational speed-up. Proc. R. Soc. A Math. Phys. Eng. Sci. 459(2036), 2011–2032 (2003)
Steane, A.: Quantum computing. Rep. Prog. Phys. 61(2), 117 (1998)
Bennett, C.H., DiVincenzo, D.P.: Quantum information and computation. Nature 404, 247 (2000)
Knill, E., Laflamme, R., Milburn, G.J.: A scheme for efficient quantum computation with linear optics. Nature 409(6816), 46–52 (2001)
Wang, S., Hou, L.L., Chen, X.F., Xu, X.F.: Continuous-variable quantum teleportation with non-Gaussian entangled states generated via multiple-photon subtraction and addition. Phys. Rev. A 91(6), 063832 (2015)
Madsen, L.S., Usenko, V.C., Lassen, M., Filip, R., Andersen, U.L.: Continuous variable quantum key distribution with modulated entangled states. Nat. Commun. 3, 1083 (2012)
Neergaard-Nielsen, J.S., Takeuchi, M., Wakui, K., Takahashi, H., Hayasaka, K., Takeoka, M., Sasaki, M.: Optical Continuous-Variable Qubit. Phys. Rev. Lett. 105(5), 053602 (2010)
Braunstein, S.L.: Quantum information with continuous variables. Rev. Mod. Phys. 77(2), 513–577 (2005)
Zavatta, A., Viciani, S., Bellini, M.: Quantum-to-classical transition with single-photon-added coherent states of light. Science 306(5696), 660–662 (2004)
Agarwal, G., Tara, K.: Nonclassical properties of states generated by the excitations on a coherent state. Phys. Rev. A 43(1), 492–497 (1991)
Kenfack, A., Zyczkowski, K.: Negativity of the Wigner function as an indicator of non-classicality. J. Opt. B Quantum Semiclass. Opt. 6(10), 396 (2004)
Bartley, T.J., Walmsley, I.A.: Directly comparing entanglement-enhancing non-Gaussian operations. New J. Phys 17(2), 023,038 (2015)
Eisert, J., Scheel, S., Plenio, M.B.: Distilling Gaussian states with gaussian operations is impossible. Phys. Rev. Lett. 89(13), 137903 (2002)
Pinheiro, P.V.P., Ramos, R.V.: Quantum communication with photon-added coherent states. Quantum Inf. Process. 12(1), 537–547 (2012)
Nogueira, K., Silva, J.B.R., Gonçalves, J.R., Vasconcelos, H.M.: Polarization and entanglement of photon-added coherent states. Phys. Rev. A 87(4), 043,821 (2013)
Wootters, W.K.: Entanglement of formation of an arbitrary state of two qubits. Phys. Rev. Lett. 80, 2245–2248 (1998)
Sanders, B.C.: Review of entangled coherent states. J. Phys. A Math. Theor. 45(24), 244002 (2012)
Sanders, B.C.: Entangled coherent states. Phys. Rev. A 45(9), 6811–6815 (1992)
Navarrete-Benlloch, C., García-Patrón, R., Shapiro, J.H., Cerf, N.J.: Enhancing quantum entanglement by photon addition and subtraction. Phys. Rev. A 86, 012328 (2012)
Nielsen, M., Chuang, I.L.: Quantum Computation and Quantum Information, 1st edn. Cambridge University Press, Cambridge (2000)
Holevo, A.S., Giovannetti, V.: Quantum channels and their entropic characteristics. Rep. Prog. Phys. 75(4), 046001 (2012)
Audretsch, J.: Entangled Systems, New Directions in Quantum Physics. Wiley-VCH Verlag GmbH, Weinheim (2008)
O’Connor, K.M., Wootters, W.K.: Entangled rings. Phys. Rev. A 63, 052302 (2001)
Jeong, H., Zavatta, A., Kang, M., Lee, Sw, Costanzo, L.S., Grandi, S., Ralph, T.C., Bellini, M.: Generation of hybrid entanglement of light. Nat. Photonics 8, 564–569 (2014)
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FDS acknowledges receipt of a PhD scholarship from CONACYT (Grant No. 331668). Thanks are due to Dr. E. Cota for useful comments on the manuscript.
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Domínguez-Serna, F.A., Mendieta-Jimenez, F.J. & Rojas, F. Entangled photon-added coherent states. Quantum Inf Process 15, 3121–3136 (2016). https://doi.org/10.1007/s11128-016-1325-9
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DOI: https://doi.org/10.1007/s11128-016-1325-9