Quantum filter processes driven by Markovian white noises have classical versions

We study quantum filters that are driven by basic quantum noises and construct classical versions. Our approach is based on exploiting the quantum markovian component of the observation and measurement processes of the filters. This approach leads in a natural way the classical versions for a class of quantum filters. We consider quantum white noises derived from Wiener and Poisson processes that drive the signal and measurement processes and derive the recursive filtering equations using classical machinery

Plane Waves in a Multispeed Discrete-Velocity Gas

A kinetic flux-splitting procedure used in conjunction with local thermodynamic equilibrium in a finite volume allows us to investigate numerically discrete-velocity gas flows. The procedure, outlined for a general discrete-velocity gas, is used to simulate flows of the nine-velocity gas, a simple two dimensional multiple-speed discrete-velocity gas, wherein a multiplicity of speeds ensures nontrivial thermodynamics. After verifying the linear wave limit and the non-linear steepening of wavefronts, the stability and propagation of planar discontinuities in that model gas is studied. The supersonic-subsonic requirement for the stable propagation of a discontinuity, being kinematic in nature is the same in the model gas, as e.g., in a perfect gas. However, the finiteness of the velocity space in the model gas does not allow a translation of the above kinematic condition to the thermodynamic requirement of increasing entropy across a compressive shock: a case of an entropy decreasing compressive shock in the model gas is presented. Finally, the interaction of various types of waves--shock waves, rarefactions and contact surfaces--in the model gas are shown in a simulation of the shock tube problem.Comment: 18 pages including u figures. All in one postscript file (plane.ps). Compressed and uuencoded (plane.uu). Name mail file `plane.uu'. Edit so that `#!/bin/csh -f' is the first line of plane.uu. On a unix machine say `csh plane.uu'. On a non-unix machine: uudecode plane.uu; uncompress plane.tar.Z; tar -xvf plane.ta

Shock structure in a nine-velocity gas

The exact structure of a shock is computed in a multiple-speed discrete-velocity gas, the nine-velocity gas, wherein the multiplicity of speeds ensures nontrivial thermodynamics. Obtained as a solution of the model Boltzmann equations, the procedure consists of tracking the shock as a trajectory of a three dimensional dynamical system connecting an equilibrium upstream state to an equilibrium downstream state. The two equilibria satisfy the jump conditions obtained from the model Euler equations. Comparison of the shock structure to that in a monatomic perfect gas, as given by the Navier-Stokes equation, shows excellent agreement. The shock in the nine-velocity gas has an overshoot in entropy alone, like in a monatomic gas. The near-equilibrium flow technique for discrete-velocity gases (Nadiga \& Pullin [2]), a kinetic flux-splitting method based on the local thermodynamic equilibrium, is also seen to capture the shock structure remarkably well.Comment: 16 pages including 4 figures and 1 table. All in one postscript file (shck.ps). Compressed and uuencoded (shck.uu). Name mail file `shck.uu'. Edit so that `#!/bin/csh -f' is the first line of shck.uu. On a unix machine say `csh shck.uu'. On a non-unix machine: uudecode adv.uu; uncompress adv.tar.Z; tar -xvf adv.ta

Propagation of correlations in Local Random Quantum Circuits

We derive a dynamical bound on the propagation of correlations in local random quantum circuits - lattice spin systems where piecewise quantum operations - in space and time - occur with classical probabilities. Correlations are quantified by the Frobenius norm of the commutator of two positive operators acting on space-like separated local Hilbert spaces. For times $t=O(L)$ correlations spread to distances $\mathcal{D}=t$ growing, at best, diffusively for any distance within that radius with extensively suppressed distance dependent corrections whereas for $t=o(L^2)$ all parts of the system get almost equally correlated with exponentially suppressed distance dependent corrections and approach the maximum amount of correlations that may be established asymptotically.Comment: 7 pages, 5 figures. Updated abstrac

Ciphertext Policy Attribute based Encryption with anonymous access policy

In Ciphertext Policy Attribute based Encryption scheme, the encryptor can fix the policy, who can decrypt the encrypted message. The policy can be formed with the help of attributes. In CP-ABE, access policy is sent along with the ciphertext. We propose a method in which the access policy need not be sent along with the ciphertext, by which we are able to preserve the privacy of the encryptor. The proposed construction is provably secure under Decision Bilinear Diffe-Hellman assumption

A Method for Near-Equilibrium Discrete-Velocity Gas Flows

We present a simulation scheme for discrete-velocity gases based on {\em local thermodynamic equilibrium}. Exploiting the kinetic nature of discrete-velocity gases, in that context, results in a natural splitting of fluxes, and the resultant scheme strongly resembles the original processes. The kinetic nature of the scheme and the modeling of the {\em infinite collision rate} limit, result in a small value of the coefficient of (numerical)-viscosity, the behavior of which is remarkably physical [18]. A first order method, and two second order methods using the total variation diminishing principle are developed and an example application presented. Given the same computer resources, it is expected that with this approach, much higher Reynold's number will be achievable than presently possible with either lattice gas automata or lattice Boltzmann approaches. The ideas being general, the scheme is applicable to any discrete-velocity model, and to lattice gases as well.Comment: 19 pages including 4 figures. All in one postscript file (flw.ps) compressed and uuencoded (flw.uu). Name mail file `flw.uu'. Edit so that `#!/bin/csh -f' is the first line of flw.uu On a unix machine say `csh flw.uu'. On a non-unix machine: uudecode flw.uu; uncompress flw.tar.Z; tar -xvf flw.ta

Steady states of continuous-time open quantum walks

Continuous-time open quantum walks (CTOQW) are introduced as the formulation of quantum dynamical semigroups of trace-preserving and completely positive linear maps (or quantum Markov semigroups) on graphs. We show that a CTOQW always converges to a steady state regardless of the initial state when a graph is connected. When the graph is both connected and regular, it is shown that the steady state is the maximally mixed state. As shown by the examples in this article, the steady states of CTOQW can be very unusual and complicated even though the underlying graphs are simple. The examples demonstrate that the structure of a graph can affect quantum coherence in CTOQW through a long time run. Precisely, the quantum coherence persists throughout the evolution of the CTOQW when the underlying topology is certain irregular graphs (such as a path or a star as shown in the examples). In contrast, the quantum coherence will eventually vanish from the open quantum system when the underlying topology is a regular graph (such as a cycle)

A New Spectral Clustering Algorithm

We present a new clustering algorithm that is based on searching for natural gaps in the components of the lowest energy eigenvectors of the Laplacian of a graph. In comparing the performance of the proposed method with a set of other popular methods (KMEANS, spectral-KMEANS, and an agglomerative method) in the context of the Lancichinetti-Fortunato-Radicchi (LFR) Benchmark for undirected weighted overlapping networks, we find that the new method outperforms the other spectral methods considered in certain parameter regimes. Finally, in an application to climate data involving one of the most important modes of interannual climate variability, the El Nino Southern Oscillation phenomenon, we demonstrate the ability of the new algorithm to readily identify different flavors of the phenomenon.Comment: 12 pages, 9 figure

Physical realization of topological quantum walks on IBM-Q and beyond

We discuss an efficient physical realization of topological quantum walks on a finite lattice. The $N$-point lattice is realized with $\log_2 N$ qubits, and the quantum circuit utilizes a number of quantum gates which is polynomial in the number of qubits. In a certain scaling limit, we show that a large number of steps is implemented with a number of quantum gates which is independent of the number of steps. We ran the quantum algorithm on the IBM-Q five-qubit quantum computer, thus experimentally demonstrating topological features, such as boundary bound states, on a lattice with $N=4$ points.Comment: 10 pages, 8 figure

Quantum routing games

We discuss the connection between a class of distributed quantum games, with remotely located players, to the counter intuitive Braess' paradox of traffic flow that is an important design consideration in generic networks where the addition of a zero cost edge decreases the efficiency of the network. A quantization scheme applicable to non-atomic routing games is applied to the canonical example of the network used in Braess' Paradox. The quantum players are modeled by simulating repeated game play. The players are allowed to sample their local payoff function and update their strategies based on a selfish routing condition in order to minimize their own cost, leading to the Wardrop equilibrium flow. The equilibrium flow in the classical network has a higher cost than the optimal flow. If the players have access to quantum resources, we find that the cost at equilibrium can be reduced to the optimal cost, resolving the paradox.Comment: 5 pages, 3 figure