We investigate the multiphoton states generated by high-gain optical parametric amplification of a single injected photon, polarization encoded as a "qubit." The experiment configuration exploits the optimal phasecovariant cloning in the high gain regime. The interference fringe pattern showing the nonlocal transfer of coherence between the injected qubit and the mesoscopic amplified output field involving up to 4000 photons has been investigated. A probabilistic method to extract full information about the multiparticle output wave function has been implemented.

Abstract. We characterise the value function of the optimal dividend problem with a finite time horizon as the unique classical solution of a suitable Hamilton-Jacobi-Bellman equation. The optimal dividend strategy is realised by a Skorokhod reflection of the fund's value at a time-dependent optimal boundary. Our results are obtained by establishing for the first time a new connection between singular control problems with an absorbing boundary and optimal stopping problems on a diffusion reflected at 0 and created at a rate proportional to its local time.

This paper analyses two-player nonzero-sum games of optimal stopping on a class of linear regular diffusions with not non-singular boundary behaviour (in the sense of Itô and McKean (1974), p. 108). We provide sufficient conditions under which Nash equilibria are realised by each player stopping the diffusion at one of the two boundary points of an interval. The boundaries of this interval solve a system of algebraic equations. We also provide conditions sufficient for the uniqueness of the equilibrium in this class.

No abstract