Title:
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Publisher Information:
Taylor \& Francis, Abingdon, Oxfordshire, 1978.
Subject Terms:
Stopping times ,
optimal stopping problems ,
gambling theory ,
Stability of difference equations ,
Canonical forms, reductions, classification ,
Deterministic scheduling theory in operations research ,
Numerical computation of matrix norms, conditioning, scaling ,
Statistical aspects of information-theoretic topics ,
Numerical methods involving duality ,
Other matrix groups over rings ,
Queueing theory (aspects of probability theory) ,
Probabilistic models, generic numerical methods in probability and statistics ,
Linear algebraic groups over arbitrary fields ,
Derived categories, triangulated categories ,
Applications of statistics to biology and medical sciences ,
meta analysis ,
Discrete-time control/observation systems ,
Nonparametric tolerance and confidence regions ,
Stability and instability of geophysical and astrophysical flows ,
Complete class results in statistical decision theory ,
Lyapunov and storage functions ,
Transform methods (e.g., integral transforms) applied to PDEs ,
Risk theory, insurance ,
Other numerical methods in calculus of variations ,
Fundamental solutions to PDEs and systems of PDEs with constant coefficients ,
Stabilization of systems by feedback ,
Systems of elliptic equations, boundary value problems ,
Combinatorial identities, bijective combinatorics ,
Theoretical approximation of solutions to ordinary differential equations ,
Measures of association (correlation, canonical correlation, etc.) ,
Sums of independent random variables ,
random walks ,
Graphs and linear algebra (matrices, eigenvalues, etc.) ,
\(H^\infty\)-control ,
Probabilistic methods, stochastic differential equations ,
Quantum measurement theory, state operations, state preparations ,
Feedback control ,
Search theory ,
Near-rings ,
Discrete location and assignment ,
Computational methods (permutation groups) ,
Reaction-diffusion equations ,
Linear inference, regression ,
Perturbations in control/observation systems ,
\(q\)-calculus and related topics ,
Numerical analysis or methods applied to Markov chains ,
Set theory ,
Set-valued operators ,
Corporate finance (dividends, real options, etc.) ,
Controllability ,
Ordinary representations and characters ,
Ridge regression ,
shrinkage estimators (Lasso) ,
Management decision making, including multiple objectives ,
Diffusion processes and stochastic analysis on manifolds ,
Matrices over special rings (quaternions, finite fields, etc.) ,
Exact enumeration problems, generating functions ,
Symbolic computation and algebraic computation ,
Parametric hypothesis testing ,
Commutativity of matrices ,
Subgroups of symmetric groups ,
Data analysis (statistics) ,
Absolute and convective instability and stability in hydrodynamic stability ,
Limit theorems in probability theory ,
Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics ,
Numerical algorithms for specific classes of architectures ,
Stochastic partial differential equations (aspects of stochastic analysis) ,
Adaptive control/observation systems ,
Nonlinear programming ,
Linear programming ,
Computational methods in Markov chains ,
Deterministic network models in operations research ,
Orbital mechanics ,
Robustness and adaptive procedures (parametric inference) ,
System identification ,
Classification and discrimination ,
cluster analysis (statistical aspects) ,
Distance in graphs ,
Applications of operator theory to differential and integral equations ,
Heat equation ,
Matrix equations and identities ,
Topological structure of integral curves, singular points, limit cycles of ordinary differential equations ,
Stochastic particle methods ,
Topology of special sets defined by functions ,
Presheaves and sheaves, stacks, descent conditions (category-theoretic aspects) ,
System structure simplification ,
Microeconomic theory (price theory and economic markets) ,
Parallel numerical computation ,
Factor analysis and principal components ,
correspondence analysis ,
Series and lattices of subgroups ,
Neutral functional-differential equations ,
Filtering in stochastic control theory ,
Statistical tables ,
Time series, auto-correlation, regression, etc. in statistics (GARCH) ,
Mathematical modelling of systems ,
Algebraic methods ,
Order statistics ,
empirical distribution functions ,
Waves and radiation in optics and electromagnetic theory ,
Iterative numerical methods for linear systems ,
Nonlinear boundary value problems for ordinary differential equations ,
Adaptive or robust stabilization ,
Sufficient statistics and fields ,
Analysis of variance and covariance (ANOVA) ,
Directed graphs (digraphs), tournaments ,
Incompressible inviscid fluids ,
General theory of rotating fluids ,
Quadratic programming ,
Enumeration in graph theory ,
Finite difference methods applied to problems in fluid mechanics ,
First-order nonlinear hyperbolic equations ,
Inference from stochastic processes and prediction ,
Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations ,
Counterexamples in general topology ,
Reliability, availability, maintenance, inspection in operations research ,
Analytic circuit theory ,
Quantum computation ,
Chain conditions on annihilators and summands: Goldie-type conditions ,
Empirical decision procedures ,
empirical Bayes procedures ,
Torsion theories ,
radicals on module categories (associative algebraic aspects) ,
Probabilistic measure theory ,
Subalgebras, congruence relations ,
Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) ,
Asymptotic approximations, asymptotic expansions (steepest descent, etc.) ,
Combinatorial aspects of partitions of integers ,
Topological linear spaces of test functions, distributions and ultradistributions ,
Transport processes in time-dependent statistical mechanics ,
Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) ,
General theory of functional-differential equations ,
Model systems in control theory ,
General topics in artificial intelligence ,
Artinian rings and modules (associative rings and algebras) ,
Systems of nonsingular linear integral equations ,
Combinatorial aspects of tessellation and tiling problems ,
Geo-electricity and geomagnetism ,
von Neumann regular rings and generalizations (associative algebraic aspects) ,
Packaged methods for numerical algorithms ,
Design of statistical experiments ,
Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs ,
Parametric inference ,
Learning and adaptive systems in artificial intelligence ,
Direct numerical and large eddy simulation of turbulence ,
Applications of statistics in engineering and industry ,
control charts ,
Computability and recursion theory ,
Dynamic programming ,
Tilings in \(2\) dimensions (aspects of discrete geometry) ,
Positive matrices and their generalizations ,
cones of matrices ,
Fixed-point theorems ,
Classical hypergeometric functions, \({}_2F_1\) ,
General nonlinear regression ,
Packing and covering in \(n\) dimensions (aspects of discrete geometry) ,
Sensitivity (robustness) ,
Recurrences ,
Statistical distribution theory ,
Input-output approaches in control theory ,
Nonparametric hypothesis testing ,
Multi-objective and goal programming ,
Computational methods in systems theory ,
Arithmetic and combinatorial problems involving abstract finite groups ,
Designs and configurations ,
Eigenvalue problems ,
Permutations, words, matrices ,
Applications of renewal theory (reliability, demand theory, etc.) ,
Group rings ,
Cohen-Macaulay modules ,
Theories of friction (tribology) ,
Exact distribution theory in statistics ,
Lasers, masers, optical bistability, nonlinear optics ,
Neural networks for/in biological studies, artificial life and related topics ,
Markov chains (discrete-time Markov processes on discrete state spaces) ,
Linearizations ,
Bounds on codes ,
Multivariate analysis ,
Sensitivity, stability, parametric optimization ,
Factorial statistical designs ,
Heat and mass transfer, heat flow ,
Simple and semisimple modules, primitive rings and ideals in associative algebras ,
General theory of difference equations ,
Production models ,
Control/observation systems governed by ordinary differential equations ,
Planetary atmospheres ,
Applications of statistics to actuarial sciences and financial mathematics ,
Boolean algebras (Boolean rings) ,
Statistical block designs ,
Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations ,
Observability ,
Combinatorial optimization ,
Bayesian inference ,
General (adjoints, conjugates, products, inverses, domains, ranges, etc.) ,
Gaussian processes ,
Regular semigroups ,
Antennas, waveguides in optics and electromagnetic theory ,
Distribution theory ,
Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems ,
Representation type (finite, tame, wild, etc.) of associative algebras ,
Planar graphs ,
geometric and topological aspects of graph theory ,
Associative rings of functions, subdirect products, sheaves of rings ,
Operations with distributions and generalized functions ,
Characteristic functions ,
other transforms ,
Derivative securities (option pricing, hedging, etc.) ,
Oscillation theory of functional-differential equations ,
Finite difference methods for initial value and initial-boundary value problems involving PDEs ,
Injective modules, self-injective associative rings ,
Models and methods for concurrent and distributed computing (process algebras, bisimulation, transition nets, etc.) ,
Applications of Lie groups to the sciences ,
explicit representations ,
Control of mechanical systems ,
Existence, uniqueness, and regularity theory for incompressible inviscid fluids ,
Magnetohydrodynamics and electrohydrodynamics ,
Theory of matrix inversion and generalized inverses ,
Group rings of finite groups and their modules (group-theoretic aspects) ,
Transformation and reduction of ordinary differential equations and systems, normal forms ,
Positional games (pursuit and evasion, etc.) ,
Dedekind, Prüfer, Krull and Mori rings and their generalizations ,
Extremal problems in graph theory ,
Representations of orders, lattices, algebras over commutative rings ,
Group rings of infinite groups and their modules (group-theoretic aspects) ,
Statistics ,
Semirings ,
Variational inequalities ,
Approximation methods and heuristics in mathematical programming ,
Other designs, configurations ,
Strange attractors, chaotic dynamics of systems with hyperbolic behavior ,
Optimal statistical designs ,
Technical applications of optics and electromagnetic theory ,
Applications of mathematical programming ,
Error bounds for initial value and initial-boundary value problems involving PDEs ,
Elliptic functions and integrals ,
Generalized functions for nonlinear analysis (Rosinger, Colombeau, nonstandard, etc.) ,
Applications of Markov renewal processes (reliability, queueing networks, etc.) ,
Testing in survival analysis and censored data ,
Models of societies, social and urban evolution ,
Spatial models in sociology ,
Random number generation in numerical analysis ,
Variable structure systems ,
Nonparametric estimation ,
Actions of groups on commutative rings ,
invariant theory ,
Social networks ,
opinion dynamics ,
Identification in stochastic control theory ,
Mathematical sociology (including anthropology) ,
Estimation in multivariate analysis ,
Integral transforms of special functions ,
Sufficiency and information ,
Nonconvex programming, global optimization ,
Weyl theory and its generalizations for ordinary differential equations ,
Existence theories for optimal control problems involving ordinary differential equations ,
Mixed integer programming ,
Compressibility effects in turbulence ,
Module categories in associative algebras ,
Sampling theory, sample surveys ,
Inference from stochastic processes and spectral analysis ,
Queues and service in operations research ,
Applications of statistics to economics ,
Characterization and structure theory for multivariate probability distributions ,
copulas ,
Other numerical methods (fluid mechanics) ,
Asymptotic distribution theory in statistics ,
Asymptotic behavior of solutions to PDEs ,
Computational problems in statistics ,
Central limit and other weak theorems ,
Software, source code, etc. for problems pertaining to statistics ,
General systems ,
Combinatorial aspects of block designs ,
Turbulence ,
Economic time series analysis ,
Computation of special functions and constants, construction of tables ,
Sequential statistical analysis ,
Bayesian problems ,
characterization of Bayes procedures ,
Hyperbolic conservation laws ,
Continuous-time Markov processes on general state spaces ,
Minimal systems representations ,
Representations of quivers and partially ordered sets ,
Automorphism groups of groups ,
Discrete version of topics in analysis ,
Orthogonal arrays, Latin squares, Room squares ,
Rods (beams, columns, shafts, arches, rings, etc.) ,
Hypothesis testing in multivariate analysis ,
Theory of statistical experiments ,
Set-valued and variational analysis ,
Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with topology, geometry and differential geometry ,
Basic theta functions ,
Inverse problems for PDEs ,
Uniqueness of solutions of equilibrium problems in solid mechanics ,
Turbulent boundary layers ,
Basic methods in fluid mechanics ,
Decision theory ,
Synthesis problems ,
Measure and integration ,
Numerical mathematical programming methods ,
Dynamics of multibody systems ,
Matrices over function rings in one or more variables ,
Einstein's equations (general structure, canonical formalism, Cauchy problems) ,
Abstract data types ,
algebraic specification ,
Ordinary differential equations in the complex domain ,
Parametric tolerance and confidence regions ,
Linear vibration theory ,
Second-order hyperbolic equations ,
Point estimation ,
Renewal theory ,
Mathematical programming ,
Attractors and repellers of smooth dynamical systems and their topological structure ,
Monte Carlo methods ,
PDEs in connection with relativity and gravitational theory ,
General and philosophical questions in quantum theory ,
Multivariable systems, multidimensional control systems ,
Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations ,
Programming involving graphs or networks ,
Stability and convergence of numerical methods for boundary value problems involving PDEs ,
Combinatorial aspects of matroids and geometric lattices ,
Existence of optimal solutions to problems involving randomness ,
Automorphisms of infinite groups ,
Theory of software ,
Traffic problems in operations research ,
Ordinary differential operators ,
KdV equations (Korteweg-de Vries equations) ,
Sequential estimation ,
Toeplitz operators, Hankel operators, Wiener-Hopf operators ,
Linear-quadratic optimal control problems ,
Fibonacci and Lucas numbers and polynomials and generalizations ,
Point processes (e.g., Poisson, Cox, Hawkes processes) ,
Finite abelian groups ,
Estimation and detection in stochastic control theory ,
Burst-correcting codes ,
Computational methods in stochastic control ,
Applications of graph theory ,
Linear ordinary differential equations and systems ,
Solvable groups, supersolvable groups ,
Navier-Stokes equations for incompressible viscous fluids ,
Stability of topological dynamical systems ,
Determinants, permanents, traces, other special matrix functions ,
Numerical solution of discretized equations for boundary value problems involving PDEs ,
Multivariate distribution of statistics ,
PDEs in connection with fluid mechanics ,
Contact in solid mechanics ,
Numerical methods for initial value problems involving ordinary differential equations ,
Atomic physics ,
Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) ,
Graph labelling (graceful graphs, bandwidth, etc.) ,
Boundary value problems for second-order elliptic equations ,
Functions of hypercomplex variables and generalized variables ,
Application models in control theory ,
Nonlinear systems in control theory ,
Radix representation ,
digital problems ,
Statistical methods ,
risk measures ,
Linear codes (general theory) ,
Asymptotic stability in control theory ,
Method of lines for initial value and initial-boundary value problems involving PDEs ,
Quantum optics ,
Generators, relations, and presentations of groups ,
Reliability and life testing ,
Linear regression ,
mixed models ,
Control/observation systems governed by partial differential equations ,
Arithmetic functions ,
related numbers ,
inversion formulas ,
Uniqueness of solutions of dynamical problems in solid mechanics ,
Existence of generalized solutions of PDE ,
Vortex flows for incompressible inviscid fluids ,
Stochastic ordinary differential equations (aspects of stochastic analysis) ,
Density estimation ,
Design techniques (robust design, computer-aided design, etc.) ,
Special properties of topological spaces ,
Linear systems in control theory ,
Finite nilpotent groups, \(p\)-groups ,
Convergence and divergence of series and sequences ,
Theoretical approximation of solutions to integral equations ,
Modules, bimodules and ideals in associative algebras ,
Sums of squares and representations by other particular quadratic forms ,
Geometric group theory ,
Additive difference equations
Document Type:
Academic journal
Article
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Further Information
Abstract
Summary: Any future quantum information machine will contain unitary operators and entangled particle states. The Hilbert space describing the action of the quantum information machine separates into a bosonic and a fermionic sector. Because the bosonic sector is of higher dimension, it is always possible to encode more information into a multiboson state than into a multifermion state, given the same complexity, that is unitary representation, of the quantum information machine. This is explicitly studied for the case of two particles defined in two modes. There the beam splitter is a generic representation of any U(2) matrix, and it has recently been shown that one can realize any \(N\)-dimensional unitary operator by successive application of such two-dimensional operators. The two-boson two-mode Hilbert space is of dimension three, and thus one can encode \(\log_23=1.57\) bits of information into such an entangled state. Finally, some explicit schemes for creating and detecting the three possible, two-photon, two-mode states spanning the bosonic Bell basis are given.