Optimizing Quantum Models of Classical Channels: The reverse Holevo problem

Given a classical channel---a stochastic map from inputs to outputs---the input can often be transformed to an intermediate variable that is informationally smaller than the input. The new channel accurately simulates the original but at a smaller transmission rate. Here, we examine this procedure when the intermediate variable is a quantum state. We determine when and how well quantum simulations of classical channels may improve upon the minimal rates of classical simulation. This inverts Holevo's original question of quantifying the capacity of quantum channels with classical resources. We also show that this problem is equivalent to another, involving the local generation of a distribution from common entanglement.Comment: 13 pages, 6 figures; http://csc.ucdavis.edu/~cmg/compmech/pubs/qfact.htm; substantially updated from v

Extreme Quantum Advantage for Rare-Event Sampling

We introduce a quantum algorithm for efficient biased sampling of the rare events generated by classical memoryful stochastic processes. We show that this quantum algorithm gives an extreme advantage over known classical biased sampling algorithms in terms of the memory resources required. The quantum memory advantage ranges from polynomial to exponential and when sampling the rare equilibrium configurations of spin systems the quantum advantage diverges.Comment: 11 pages, 9 figures; http://csc.ucdavis.edu/~cmg/compmech/pubs/eqafbs.ht

h-deformation of Gr(2)

The $h$-deformation of functions on the Grassmann matrix group $Gr(2)$ is presented via a contraction of $Gr_q(2)$. As an interesting point, we have seen that, in the case of the $h$-deformation, both R-matrices of $GL_h(2)$ and $Gr_h(2)$ are the same

Phase transition in an asymmetric generalization of the zero-temperature Glauber model

An asymmetric generalization of the zero-temperature Glauber model on a lattice is introduced. The dynamics of the particle-density and specially the large-time behavior of the system is studied. It is shown that the system exhibits two kinds of phase transition, a static one and a dynamic one.Comment: LaTeX, 9 pages, to appear in Phys. Rev. E (2001

Reconstructing f(R) model from Holographic DE: Using the observational evidence

We investigate the corresponding relation between $f(R)$ gravity and an interacting holographic dark energy. By obtaining conditions needed for some observational evidence such as, positive acceleration expansion of universe, crossing the phantom divide line and validity of thermodynamics second law in an interacting HDE model and corresponding it with $f(R)$ mode of gravity we find a viable $f(R)$ model which can explain the present universe. We also obtain the explicit evolutionary forms of the corresponding scalar field, potential and scale factor of universe.Comment: 11page. phys. Scr (2012

On the effect of scalarising norm choice in a ParEGO implementation

Computationally expensive simulations play an increasing role in engineering design, but their use in multi-objective optimization is heavily resource constrained. Specialist optimizers, such as ParEGO, exist for this setting, but little knowledge is available to guide their configuration. This paper uses a new implementation of ParEGO to examine three hypotheses relating to a key configuration parameter: choice of scalarising norm. Two hypotheses consider the theoretical trade-off between convergence speed and ability to capture an arbitrary Pareto front geometry. Experiments confirm these hypotheses in the bi-objective setting but the trade-off is largely unseen in many-objective settings. A third hypothesis considers the ability of dynamic norm scheduling schemes to overcome the trade-off. Experiments using a simple scheme offer partial support to the hypothesis in the bi-objective setting but no support in many-objective contexts. Norm scheduling is tentatively recommended for bi-objective problems for which the Pareto front geometry is concave or unknown

RTT relations, a modified braid equation and noncommutative planes

With the known group relations for the elements $(a,b,c,d)$ of a quantum matrix $T$ as input a general solution of the $RTT$ relations is sought without imposing the Yang - Baxter constraint for $R$ or the braid equation for $\hat{R} = PR$. For three biparametric deformatios, $GL_{(p,q)}(2), GL_{(g,h)}(2)$ and $GL_{(q,h)}(1/1)$, the standard,the nonstandard and the hybrid one respectively, $R$ or $\hat{R}$ is found to depend, apart from the two parameters defining the deformation in question, on an extra free parameter $K$,such that only for two values of $K$, given explicitly for each case, one has the braid equation. Arbitray $K$ corresponds to a class (conserving the group relations independent of $K$) of the MQYBE or modified quantum YB equations studied by Gerstenhaber, Giaquinto and Schak. Various properties of the triparametric $\hat{R}(K;p,q)$, $\hat{R}(K;g,h)$ and $\hat{R}(K;q,h)$ are studied. In the larger space of the modified braid equation (MBE) even $\hat{R}(K;p,q)$ can satisfy $\hat{R}^2 = 1$ outside braid equation (BE) subspace. A generalized, $K$- dependent, Hecke condition is satisfied by each 3-parameter $\hat{R}$. The role of $K$ in noncommutative geometries of the $(K;p,q)$,$(K;g,h)$ and $(K;q,h)$ deformed planes is studied. K is found to introduce a "soft symmetry breaking", preserving most interesting properties and leading to new interesting ones. Further aspects to be explored are indicated.Comment: Latex, 17 pages, minor change

On a "New" Deformation of GL(2)

We refute a recent claim in the literature of a "new" quantum deformation of GL(2).Comment: 4 pages, LATE

Revised spherically symmetric solutions of R+ε/RR+\varepsilon/R gravity

We study spherically symmetric static empty space solutions in $R+\varepsilon/R$ model of $f(R)$ gravity. We show that the Schwarzschild metric is an exact solution of the resulted field equations and consequently there are general solutions which {are perturbed Schwarzschild metric and viable for solar system. Our results for large scale contains a logarithmic term with a coefficient producing a repulsive gravity force which is in agreement with the positive acceleration of the universe.Comment: 8 page