Experimentally realizable characterizations of continuous variable Gaussian states

Measures of entanglement, fidelity and purity are basic yardsticks in quantum information processing. We propose how to implement these measures using linear devices and homodyne detectors for continuous variable Gaussian states. In particular, the test of entanglement becomes simple with some prior knowledge which is relevant to current experiments.Comment: 4 pages, This paper supersedes quant-ph/020315

Solution of a one-dimensional stochastic model with branching and coagulation reactions

We solve an one-dimensional stochastic model of interacting particles on a chain. Particles can have branching and coagulation reactions, they can also appear on an empty site and disappear spontaneously. This model which can be viewed as an epidemic model and/or as a generalization of the {\it voter} model, is treated analytically beyond the {\it conventional} solvable situations. With help of a suitably chosen {\it string function}, which is simply related to the density and the non-instantaneous two-point correlation functions of the particles, exact expressions of the density and of the non-instantaneous two-point correlation functions, as well as the relaxation spectrum are obtained on a finite and periodic lattice.Comment: 5 pages, no figure. To appear as a Rapid Communication in Physical Review E (September 2001

Entangled light in transition through the generation threshold

We investigate continuous variable entangling resources on the base of two-mode squeezing for all operational regimes of a nondegenerate optical parametric oscillator with allowance for quantum noise of arbitrary level. The results for the quadrature variances of a pair of generated modes are obtained by using the exact steady-state solution of Fokker-Planck equation for the complex P-quasiprobability distribution function. We find a simple expression for the squeezed variances in the near-threshold range and conclude that the maximal two-mode squeezing reaches 50% relative to the level of vacuum fluctuations and is achieved at the pump field intensity close to the generation threshold. The distinction between the degree of two-mode squeezing for monostable and bistable operational regimes is cleared up.Comment: 7 pages, 4 figures; Content changed: more details added to the discussion. To be published in Phys. Rev.

Dynamics of entanglement between two trapped atoms

We investigate the dynamics of entanglement between two continuous variable quantum systems. The model system consists of two atoms in a harmonic trap which are interacting by a simplified s-wave scattering. We show, that the dynamically created entanglement changes in a steplike manner. Moreover, we introduce local operators which allow us to violate a Bell-CHSH inequality adapted to the continuous variable case. The correlations show nonclassical behavior and almost reach the maximal quantum mechanical value. This is interesting since the states prepared by this interaction are very different from any EPR-like state.Comment: 9 page

The Ten Martini Problem

We prove the conjecture (known as the ``Ten Martini Problem'' after Kac and Simon) that the spectrum of the almost Mathieu operator is a Cantor set for all non-zero values of the coupling and all irrational frequencies.Comment: 31 pages, no figure

Characterizing the entanglement of bipartite quantum systems

We derive a separability criterion for bipartite quantum systems which generalizes the already known criteria. It is based on observables having generic commutation relations. We then discuss in detail the relation among these criteria.Comment: 5 pages, 2 figures. Revised versio

Generalised quantum weakest preconditions

Generalisation of the quantum weakest precondition result of D'Hondt and Panangaden is presented. In particular the most general notion of quantum predicate as positive operator valued measure (POVM) is introduced. The previously known quantum weakest precondition result has been extended to cover the case of POVM playing the role of a quantum predicate. Additionally, our result is valid in infinite dimension case and also holds for a quantum programs defined as a positive but not necessary completely positive transformations of a quantum states.Comment: 7 pages, no figures, added references, changed conten

Demonstrating various quantum effects with two entangled laser beams

We report on the preparation of entangled two mode squeezed states of yet unseen quality. Based on a measurement of the covariance matrix we found a violation of the Reid and Drummond EPR-criterion at a value of only 0.36\pm0.03 compared to the threshold of 1. Furthermore, quantum state tomography was used to extract a single photon Fock state solely based on homodyne detection, demonstrating the strong quantum features of this pair of laser-beams. The probability for a single photon in this ensemble measurement exceeded 2/3

Phase diagram of the one-dimensional extended attractive Hubbard model for large nearest-neighbor repulsion

We consider the extended Hubbard model with attractive on-site interaction U and nearest-neighbor repulsions V. We construct an effective Hamiltonian H_{eff} for hopping t<<V and arbitrary U<0. Retaining the most important terms, H_{eff} can be mapped onto two XXZ models, solved by the Bethe ansatz. The quantum phase diagram shows two Luttinger liquid phases and a region of phase separation between them. For density n<0.422 and U<-4, singlet superconducting correlations dominate at large distances. For some parameters, the results are in qualitative agreement with experiments in BaKBiO.Comment: 6 pages, 3 figures, submitted to Phys. Rev.

Correlation Functions for Diffusion-Limited Annihilation, A + A -> 0

The full hierarchy of multiple-point correlation functions for diffusion-limited annihilation, A + A -> 0, is obtained analytically and explicitly, following the method of intervals. In the long time asymptotic limit, the correlation functions of annihilation are identical to those of coalescence, A + A -> A, despite differences between the two models in other statistical measures, such as the interparticle distribution function