Cloning and cryptography with quantum continuous variables
École Polytechnique, CP 165, Université Libre de Bruxelles, 1050 Brussels, Belgium
2 Jet Propulsion Laboratory, California Institute of Technology, Pasadena CA 91109, USA
Corresponding author: a firstname.lastname@example.org
Published online: 15 February 2002
The cloning of quantum variables with continuous spectra is investigated. We define a Gaussian 1-to-2 cloning machine that copies equally well two conjugate variables such as position and momentum or the two quadrature components of a light mode. The resulting cloning fidelity for coherent states, namely F=2/3, is shown to be optimal. An asymmetric version of this Gaussian cloner is then used to assess the security of a continuous-variable quantum key distribution scheme that allows two remote parties to share a Gaussian key. The information versus disturbance tradeoff underlying this continuous quantum cryptographic scheme is then analyzed for the optimal individual attack. Methods to convert the resulting Gaussian keys into secret key bits are also studied. Finally, the extension of the Gaussian cloner to optimal N-to-M continuous cloners is discussed, and it is shown how to implement these cloners for light modes using a phase-insensitive optical amplifier and beam splitters. In addition, a phase-conjugate input cloner is defined, yielding M clones and M' anticlones from N replicas of a coherent state and N' replicas of its phase-conjugate (with ). This novel kind of cloners is shown to outperform the standard N-to-M cloners in some cases.
PACS: 03.67.Dd – Quantum cryptography / 42.50.-p – Quantum optics / 89.70.+c – Information science
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2002