Quantum conditional cloning of continuous variable entangled states

K. Liu; J. R. Gao

doi:10.2971/jeos.2014.14057

Journal of the European Optical Society - Rapid publications, Vol 9 (2014)

Quantum conditional cloning of continuous variable entangled states

K. Liu, J. R. Gao

Abstract

We extend the technique of conditional preparation to a quantum cloning machine, and present a protocol of 1 -> 2 conditional cloning of squeezed state and entanglement states. It is shown that the entanglement degree of the cloned entangled states can be well preserved even when the fidelity between the input and output states is beyond the limit of 4/9. This scheme is practicable since only the linear elements of beam splitters, homodyne detections, optical modulations and electrical trigger system, are involved.

Full Text: PDF

Citation Details

Cite this article

References

W. K. Wooters, and W. H. Zurek, ”A single quantum cannot be cloned,” Nature 299, 802–803 (1982).

V. Buˇzek, and M. Hillery, ”Quantum copying: beyond the nocloning theorem,” Phys. Rev. A 54, 1844–1852 (1996).

V. Buˇzek, and M. Hillery, ”Universal optimal cloning of arbitrary quantum states: from qubits to quantum registers,” Phys. Rev. Lett. 81, 5003–5006 (1998).

N. J. Cerf, A. Ipe, and X. Rottenberg, ”Cloning of continuous quantum variables,” Phys. Rev. Lett. 85, 1754–1757 (2000).

Z. Zhai, J. Guo, and J. R. Gao, ”Generalization of continuousvariable quantum cloning with linear optics,” Phys. Rev. A 73, 052302 (2006).

J. Fiurásek, ”Optical implementation of continuous-variable quantum cloning machines,” Phys. Rev. Lett. 86, 4942–4945 (2001).

S. L. Braunstein, N. J. Cerf, S. Iblisdir, P. van Loock, and S. Massar, ”Optimal cloning of coherent states with a linear amplifier and beam splitters,” Phys. Rev. Lett. 86, 4938–4941 (2001).

N. J. Cerf, O. Krüger, P. Navez, R. F. Werner, and M. M. Wolf, ”Non-Gaussian cloning of quantum coherent states is optimal,” Phys. Rev. Lett. 95, 070501 (2005).

S. Olivares, M. G. A. Paris, and U. L. Andersen, ”Cloning of Gaussian states by linear optics,” Phys. Rev. A 73, 062330 (2006).

U. L. Andersen, V. Josse, and G. Leuchs, ”Unconditional quantum cloning of coherent states with linear optics,” Phys. Rev. Lett. 94, 240503 (2005).

M. Sabuncu, U. L. Andersen, and G. Leuchs, ”Experimental demonstration of continuous variable cloning with phase-conjugate inputs,” Phys. Rev. Lett. 98, 170503 (2007).

A. Einstein, B. Podolsky, and N. Rosen, ”Can quantum-mechanical description of physical reality be considered complete?,” Phys. Rev. 47, 777–780 (1935).

Z. Y. Ou, S. F. Pereira, H. J. Kimble, and K. C. Peng, ”Realization of the Einstein-Podolsky-Rosen paradox for continuous variables,” Phys. Rev. Lett. 68, 3663–3666 (1992).

M. D. Reid, and P. D. Drummond, ”Quantum correlations of phase in nondegenerate parametric oscillation,” Phys. Rev. Lett. 60, 2731–2733 (1988).

A. Furusawa, J. L. Sørensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, ”Unconditional quantum teleportation,” Science 282, 706–709 (1998).

J. Jing, J. Zhang, Y. Yan, F. Zhao, C. D. Xie, and K. C. Peng, ”Experimental demonstration of tripartite entanglement and controlled dense coding for continuous variables,” Phys. Rev. Lett. 90, 167903 (2003).

C. Silberhorn, N. Korolkova, and G. Leuchs, ”Quantum key distribution with bright entangled beams,” Phys. Rev. Lett. 88, 167902 (2002).

N. C. Menicucci, P. van Loock, M. Gu, C. Weedbrook, T. C. Ralph, and M. A. Nielsen, ”Universal quantum computation with continuous-variable cluster states,” Phys. Rev. Lett. 97, 110501 (2006).

C. Weedbrook, A. M. Lance, W. P. Bowen, T. Symul, T. C. Ralph, and P. K. Lam, ”Coherent-state quantum key distribution without random basis switching,” Phys. Rev. A 73, 022316 (2006).

C. Weedbrook, N. B. Grosse, T. Symul, P. K. Lam, and T. C. Ralph, ”Quantum cloning of continuous-variable entangled states,” Phys. Rev. A 77, 052313 (2008).

J. Laurat, T. Coudreau, N. Treps, A. Maître, and C. Fabre, ”Conditional preparation of a quantum state in the continuous variable regime: generation of a sub-Poissonian state from twin beams,” Phys. Rev. Lett. 91, 213601 (2003).

J. Laurat, T. Coudreau, N. Treps, A. Maître and C. Fabre, ”Conditional preparation of a nonclassical state in the continuousvariable regime: theoretical study,” Phys. Rev. A 69, 033808 (2004).

A. Franzen, B. Hage, J. DiGuglielmo, J. Fiuráˇsek, and R. Schnabel, ”Experimental demonstration of continuous variable purification of squeezed states,” Phys. Rev. Lett. 97, 150505 (2006).

B. Hage, A. Samblowski, J. DiGuglielmo, A. Franzen, J. Fiuráˇsek, and R. Schnabel, ”Preparation of distilled and purified continuousvariable entangled states,” Nat. Phys. 4, 915–918 (2008).

R. Dong, M. Lassen, J. Heersink, C. Marquardt, R. Filip, G. Leuchs, and U. L. Andersen, ”Experimentally entanglement distillation of mesoscopic quantum states,” Nat. Phys. 4, 919–923 (2008).

H. Takahashi, J. S. Neergaard-Nielsen, M. Takeuchi, M. Takeoka, K. Hayasaka, A. Furusawa, and M. Sasaki, ”Entanglement distillation from Gaussian input states,” Nat. Photonics 4, 178–181 (2010).

R. Jozsa, ”Fidelity for mixed quantum states,” J. Mod. Optic. 41, 2315–2323 (1994).

H. Zhang, W. Liang, K. Liu, J. X. Zhang, and J. R. Gao, ”Fidelity with quadrature component variances for continuous variable quantum teleportation,” J. Phys. B 45, 115501 (2012).

S. L. Braunstein, and H. J. Kimble, ”Teleportation of continuous quantum variables,” Phys. Rev. Lett. 80, 869–872 (1998).

L. M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, ”Inseparability criterion for continuous variable systems,” Phys. Rev. Lett. 84, 2722–2725 (2000).

J. Fiuráˇsek, P. Marek, R. Filip, and R. Schnabel, ”Experimentally feasible purification of continuous-variable entanglement,” Phys. Rev. A 75, 050302 (2007).

M. Lassen, L. S. Madsen, M. Sabuncu, R. Filip, and U. L. Andersen, ”Experimental demonstration of squeezed-state quantum averaging,” Phys. Rev. A 82, 021801(R) (2010).

L. M. Duan, and G. C. Guo, ”Probabilistic cloning and identification of linearly independent quantum states,” Phys. Rev. Lett. 80, 4999–5002 (1998).