Upper bounds on entangling rates of bipartite Hamiltonians

We discuss upper bounds on the rate at which unitary evolution governed by a non-local Hamiltonian can generate entanglement in a bipartite system. Given a bipartite Hamiltonian H coupling two finite dimensional particles A and B, the entangling rate is shown to be upper bounded by c*log(d)*norm(H), where d is the smallest dimension of the interacting particles, norm(H) is the operator norm of H, and c is a constant close to 1. Under certain restrictions on the initial state we prove analogous upper bound for the ancilla-assisted entangling rate with a constant c that does not depend upon dimensions of local ancillas. The restriction is that the initial state has at most two distinct Schmidt coefficients (each coefficient may have arbitrarily large multiplicity). Our proof is based on analysis of a mixing rate -- a functional measuring how fast entropy can be produced if one mixes a time-independent state with a state evolving unitarily.Comment: 14 pages, 4 figure

Quantum walk on the line: entanglement and non-local initial conditions

The conditional shift in the evolution operator of a quantum walk generates entanglement between the coin and position degrees of freedom. This entanglement can be quantified by the von Neumann entropy of the reduced density operator (entropy of entanglement). In the long time limit, it converges to a well defined value which depends on the initial state. Exact expressions for the asymptotic (long-time) entanglement are obtained for (i) localized initial conditions and (ii) initial conditions in the position subspace spanned by the +1 and -1 position eigenstates.Comment: A few mistakes where corrected. One of them leads to a factor of 2 in eq. (49), the other results remain unchanged. In this version, several figures where replaced by color version

Numerical Analysis of the Capacities for Two-Qubit Unitary Operations

We present numerical results on the capacities of two-qubit unitary operations for creating entanglement and increasing the Holevo information of an ensemble. In all cases tested, the maximum values calculated for the capacities based on the Holevo information are close to the capacities based on the entanglement. This indicates that the capacities based on the Holevo information, which are very difficult to calculate, may be estimated from the capacities based upon the entanglement, which are relatively straightforward to calculate.Comment: 9 pages, 10 figure

Universal quantum computation by discontinuous quantum walk

Quantum walks are the quantum-mechanical analog of random walks, in which a quantum `walker' evolves between initial and final states by traversing the edges of a graph, either in discrete steps from node to node or via continuous evolution under the Hamiltonian furnished by the adjacency matrix of the graph. We present a hybrid scheme for universal quantum computation in which a quantum walker takes discrete steps of continuous evolution. This `discontinuous' quantum walk employs perfect quantum state transfer between two nodes of specific subgraphs chosen to implement a universal gate set, thereby ensuring unitary evolution without requiring the introduction of an ancillary coin space. The run time is linear in the number of simulated qubits and gates. The scheme allows multiple runs of the algorithm to be executed almost simultaneously by starting walkers one timestep apart.Comment: 7 pages, revte

Accumulator for shaft encoder

Digital accumulator relies almost entirely on integrated circuitry to process the data derived from the outputs of gyro shaft encoder. After the read command is given, the output register collects and stores the data that are on the set output terminals of the up-down counters

Connecting the discrete and continuous-time quantum walks

Recently, quantized versions of random walks have been explored as effective elements for quantum algorithms. In the simplest case of one dimension, the theory has remained divided into the discrete-time quantum walk and the continuous-time quantum walk. Though the properties of these two walks have shown similarities, it has remained an open problem to find the exact relation between the two. The precise connection of these two processes, both quantally and classically, is presented. Extension to higher dimensions is also discussed.Comment: 5 pages, 1 figur

Application of DOT-MORSE coupling to the analysis of three-dimensional SNAP shielding problems

The use of discrete ordinates and Monte Carlo techniques to solve radiation transport problems is discussed. A general discussion of two possible coupling schemes is given for the two methods. The calculation of the reactor radiation scattered from a docked service and command module is used as an example of coupling discrete ordinates (DOT) and Monte Carlo (MORSE) calculations

Wave Profile for Anti-force Waves with Maximum Possible Currents

In the theoretical investigation of the electrical breakdown of a gas, we apply a one-dimensional, steady state, constant velocity, three component fluid model and consider the electrons to be the main element in propagation of the wave. The electron gas temperature, and therefore the electron gas partial pressure, is considered to be large enough to provide the driving force. The wave is considered to have a shock front, followed by a thin dynamical transition region. Our set of electron fluid-dynamical equations consists of the equations of conservation of mass, momentum, and energy, plus the Poisson\u27s equation. The set of equations is referred to as the electron fluid dynamical equations; and a successful solution therefor must meet a set of acceptable physical conditions at the trailing edge of the wave. For breakdown waves with a significant current behind the shock front, modifications must be made to the set of electron fluid dynamical equations, as well as the shock condition on electron temperature. Considering existence of current behind the shock front, we have derived the shock condition on electron temperature, and for a set of experimentally measured wave speeds, we have been able to find maximum current values for which solutions to our set of electron velocity, electron temperature, and electron number density within the dynamical transition region of the wave

The Perfect Distinguishability of Quantum Operations

We provide a feasible necessary and sufficient condition for when an unknown quantum operation (quantum device) secretely selected from a set of known quantum operations can be identified perfectly within a finite number of queries, and thus complete the characterization of the perfect distinguishability of quantum operations. We further design an optimal protocol which can achieve the perfect discrimination between two quantum operations by a minimal number of queries. Interestingly, employing the techniques from the theory of $q$-numerical range we find that an optimal perfect discrimination between two isometries is always achievable without using auxiliary systems or entanglement.Comment: 6.25 pages (Revtex 4), a preliminary version. Comments are welcom