Doubly infinite separation of quantum information and communication

We prove the existence of (one-way) communication tasks with a subconstant versus superconstant asymptotic gap, which we call "doubly infinite," between their quantum information and communication complexities. We do so by studying the exclusion game [C. Perry et al., Phys. Rev. Lett. 115, 030504 (2015)] for which there exist instances where the quantum information complexity tends to zero as the size of the input $n$ increases. By showing that the quantum communication complexity of these games scales at least logarithmically in $n$, we obtain our result. We further show that the established lower bounds and gaps still hold even if we allow a small probability of error. However in this case, the $n$-qubit quantum message of the zero-error strategy can be compressed polynomially.Comment: 16 pages, 2 figures. v4: minor errors fixed; close to published version; v5: financial support info adde

Conic approach to quantum graph parameters using linear optimization over the completely positive semidefinite cone

We investigate the completely positive semidefinite cone $\mathcal{CS}_+^n$, a new matrix cone consisting of all $n\times n$ matrices that admit a Gram representation by positive semidefinite matrices (of any size). In particular we study relationships between this cone and the completely positive and doubly nonnegative cones, and between its dual cone and trace positive non-commutative polynomials. We use this new cone to model quantum analogues of the classical independence and chromatic graph parameters $\alpha(G)$ and $\chi(G)$, which are roughly obtained by allowing variables to be positive semidefinite matrices instead of $0/1$ scalars in the programs defining the classical parameters. We can formulate these quantum parameters as conic linear programs over the cone $\mathcal{CS}_+^n$. Using this conic approach we can recover the bounds in terms of the theta number and define further approximations by exploiting the link to trace positive polynomials.Comment: Fixed some typo

Thermally induced instability of a doubly quantized vortex in a Bose-Einstein condensate

We study the instability of a doubly quantized vortex topologically imprinted on $^{23}$Na condensate, as reported in recent experiment [Phys. Rev. Lett. \textbf{93}, 160406 (2004)]. We have performed numerical simulations using three-dimensional Gross-Pitaevskii equation with classical thermal noise. Splitting of a doubly quantized vortex turns out to be a process that is very sensitive to the presence of thermal atoms. We observe that even ve ry small thermal fluctuations, corresponding to 10 to 15% of thermal atoms, ca use the decay of doubly quantized vortex into two singly quantized vortices in tens of milliseconds. As in the experiment, the lifetime of doubly quantized vortex i s a monotonic function of the interaction strength.Comment: 4 pages, 5 figure

Doubly excited ferromagnetic spin-chain as a pair of coupled kicked rotors

We show that the dynamics of a doubly-excited 1D Heisenberg ferromagnetic chain, subject to short pulses from a parabolic magnetic field may be analyzed as a pair of quantum kicked rotors. By focusing on the two-magnon dynamics in the kicked XXZ model we investigate how the anisotropy parameter - which controls the strength of the magnon-magnon interaction - changes the nature of the coupling between the two "image" coupled Kicked Rotors. We investigate quantum state transfer possibilities and show that one may control whether the spin excitations are transmitted together, or separate from each other.Comment: 8 pages, 4 figures; extended appendix and corrected typo

Ab Initio Calculations on the H_(2)+D_(2)=2HD Four‐Center Exchange Reaction. I. Elements of the Reaction Surface

We present the results of ab initio calculations on some interesting regions of the reaction surface for the four‐center exchange reaction H_(2)+D_(2)=2HD. These calculations, which use a minimum basis set of Slater orbitals, indicate that for all geometries appropriate to the transition state of the reaction, a barrier height of at least 148 kcal/mole is present. This is far greater than the energy required to produce free radicals and more than three times the experimental energy of activation, 42 kcal/mole. Considering the sources and magnitudes for errors due to correlation and basis set restrictions, we estimate the barrier height for this exchange reaction to be 132 ± 20 kcal/mole exclusive of zero‐point energies. In this paper we discuss the surface as determined by configuration interaction techniques. We find that the most favorable geometries for the exchange reactions are the square, rhombus, and kite configurations. However, all of these states are unstable with respect to H_(2) + 2H. In addition we find no evidence of collision complexes for any of the likely transition state geometries. In the following paper we will examine the G1 wavefunctions for this system in order to obtain an understanding of the factors responsible for the shape of the surface

Generic spectral properties of right triangle billiards

This article presents a new method to calculate eigenvalues of right triangle billiards. Its efficiency is comparable to the boundary integral method and more recently developed variants. Its simplicity and explicitness however allow new insight into the statistical properties of the spectra. We analyse numerically the correlations in level sequences at high level numbers (>10^5) for several examples of right triangle billiards. We find that the strength of the correlations is closely related to the genus of the invariant surface of the classical billiard flow. Surprisingly, the genus plays and important role on the quantum level also. Based on this observation a mechanism is discussed, which may explain the particular quantum-classical correspondence in right triangle billiards. Though this class of systems is rather small, it contains examples for integrable, pseudo integrable, and non integrable (ergodic, mixing) dynamics, so that the results might be relevant in a more general context.Comment: 18 pages, 8 eps-figures, revised: stylistic changes, improved presentatio

The Skyrme Interaction in finite nuclei and nuclear matter

Self-consistent mean-field models are a powerful tool in the investigation of nuclear structure and low-energy dynamics. They are based on effective energy-density functionals, often formulated in terms of effective density-dependent nucleon-nucleon interactions. The free parameters of the functional are adjusted to empirical data. A proper choice of these parameters requires a comprehensive set of constraints covering experimental data on finite nuclei, concerning static as well as dynamical properties, empirical characteristics of nuclear matter, and observational information on nucleosynthesis, neutron stars and supernovae. This work aims at a comprehensive survey of the performance of one of the most successful non-relativistic self-consistent method, the Skyrme-Hartree-Fock model (SHF), with respect to these constraints. A full description of the Skyrme functional is given and its relation to other effective interactions is discussed. The validity of the application of SHF far from stability and in dense environments beyond the nuclear saturation density is critically assessed. The use of SHF in models extended beyond the mean field approximation by including some correlations is discussed. Finally, future prospects for further development of SHF towards a more consistent application of the existing and promisingly newly developing constraints are outlined.Comment: 71 pages, 22 figures. Accepted for publication in Prog.Part.Nucl.Phy

Magnetic-Moment Fragmentation and Monopole Crystallization

The Coulomb phase, with its dipolar correlations and pinch-point-scattering patterns, is central to discussions of geometrically frustrated systems, from water ice to binary and mixed-valence alloys, as well as numerous examples of frustrated magnets. The emergent Coulomb phase of lattice-based systems has been associated with divergence-free fields and the absence of long-range order. Here, we go beyond this paradigm, demonstrating that a Coulomb phase can emerge naturally as a persistent fluctuating background in an otherwise ordered system. To explain this behavior, we introduce the concept of the fragmentation of the field of magnetic moments into two parts, one giving rise to a magnetic monopole crystal, the other a magnetic fluid with all the characteristics of an emergent Coulomb phase. Our theory is backed up by numerical simulations, and we discuss its importance with regard to the interpretation of a number of experimental results

Classical capacity of a qubit depolarizing channel with memory

The classical product state capacity of a noisy quantum channel with memory is investigated. A forgetful noise-memory channel is constructed by Markov switching between two depolarizing channels which introduces non-Markovian noise correlations between successive channel uses. The computation of the capacity is reduced to an entropy computation for a function of a Markov process. A reformulation in terms of algebraic measures then enables its calculation. The effects of the hidden-Markovian memory on the capacity are explored. An increase in noise-correlations is found to increase the capacity