Related papers: Conditional Distributions for Quantum Systems
In the presence of modeling errors, the mainstream Bayesian methods seldom give a realistic account of uncertainties as they commonly underestimate the inherent variability of parameters. This problem is not due to any misconception in the…
We use a novel form of quantum conditional probability to define new measures of quantum information in a dynamical context. We explore relationships between our new quantities and standard measures of quantum information, such as von…
Bayes' rule tells us how to invert a causal process in order to update our beliefs in light of new evidence. If the process is believed to have a complex compositional structure, we may observe that the inversion of the whole can be…
We study a class of parabolic quasilinear systems, in which the diffusion matrix is not uniformly elliptic, but satisfies a Petrovskii condition of positivity of the real part of the eigenvalues. Local well-posedness is known since the work…
The mathematical theory of quantum feedback networks has recently been developed for general open quantum dynamical systems interacting with bosonic input fields. In this article we show, for the special case of linear dynamical systems…
We consider Markov chains on partially ordered sets that generalize the success-runs and remaining life chains in reliability theory. We find conditions for recurrence and transience and give simple expressions for the invariant…
We give a recursive construction of the stationary distribution of multi-type asymmetric simple exclusion processes on a finite ring or on the infinite line $Z$. The construction can be interpreted in terms of "multi-line diagrams" or…
The partial transpose map is a linear map widely used quantum information theory. We study the equality condition for a matrix inequality generated by partial transpose, namely $\rank(\sum^K_{j=1} A_j^T \otimes B_j)\le K \cdot…
A sequential importance sampling algorithm is developed for the distribution that results when a matrix of independent, but not identically distributed, Bernoulli random variables is conditioned on a given sequence of row and column sums.…
We establish sufficient conditions for exponential convergence to a unique quasi-stationary distribution in the total variation norm. These conditions also ensure the existence and exponential ergodicity of the Q-process, the process…
We propose a probabilistic enhancement of standard kernel Support Vector Machines for binary classification, in order to address the case when, along with given data sets, a description of uncertainty (e.g., error bounds) may be available…
We propose a new class of models for random permutations, which we call log-linear models, by the analogy with log-linear models used in the analysis of contingency tables. As a special case, we study the family of all Luce-decomposable…
The article provides a framework to solve linear differential equations based on partial commutativity which is introduced by means of the Fedorov theorem. The framework is applied to specific types of three-level and four-level quantum…
In quantum experiments the acquisition and representation of basic experimental information is governed by the multinomial probability distribution. There exist unique random variables, whose standard deviation becomes asymptotically…
Conditional specification of distributions is a developing area with increasing applications. In the finite discrete case, a variety of compatible conditions can be derived. In this paper, we propose an alternative approach to study the…
We present a general method to derive entanglement breaking (EB) conditions for continuous-variable quantum gates. We start with an arbitrary entanglement witness, and reach an EB condition. The resultant EB condition is applicable not only…
Conditional domain generation is a good way to interactively control sample generation process of deep generative models. However, once a conditional generative model has been created, it is often expensive to allow it to adapt to new…
Exotic stochastic processes are shown to emerge in the quantum evolution of complex systems. Using influence function techniques, we consider the dynamics of a system coupled to a chaotic subsystem described through random matrix theory. We…
The sample-based Gibbs sampler has been the dominant method for approximating joint distribution from a collection of compatible full-conditional distributions. However for conditionally specified model, mixtures of incompatible full and…
A new class of random composition structures (the ordered analog of Kingman's partition structures) is defined by a regenerative description of component sizes. Each regenerative composition structure is represented by a process of random…