"A Solvable Hamiltonian System" Integrability and Action-Angle Variables

We prove that the dynamical system charaterized by the Hamiltonian $H = \lambda N \sum_{j}^{N} p_j + \mu \sum_{j,k}^{N} {{(p_j p_k)}^{1\over 2}} \{ cos [ \nu ( q_j - q_k)] \}$ proposed and studied by Calogero [1,2] is equivalent to a system of {\it non-interacting} harmonic oscillators. We find the explicit form of the conserved currents which are in involution. We also find the action-angle variables and solve the initial value problem in simple form.Comment: 12 pages, Latex, No Figure

Reply to Comment on ''Quantum key distribution for d-level systems with generalized Bell states''

In a recent comment \cite{ch1} it has been claimed that an entangled-based quantum key distribution protocol proposed in \cite{zhang} and its generalization to d-level systems in \cite{v1} are insecure against an attack devised by the authors of the comment. We invalidate the arguments of the comment and show that the protocols are still secure.Comment: 4 pages, Latex, no figures, Accepted for Publication in Phys. Rev.