Related papers: Bayes' theorem and quantum retrodiction
Predictions for measurement outcomes in physical theories are usually computed by combining two distinct notions: a state, describing the physical system, and an observable, describing the measurement which is performed. In quantum theory,…
The outcome statistics of an informationally complete quantum measurement for a system in a given state can be used to evaluate the ensemble expectation of any linear operator in the same state, by averaging a function of the outcomes that…
Estimating the state of an open quantum system monitored over time requires incorporating information from past measurements (filtering) and, for improved accuracy, also from future measurements (smoothing). While classical smoothing is…
We derive the master equation that governs the evolution of the measured state backwards in time in an open system. This allows us to determine probabilities for a given set of preparation events from the results of subsequent measurements,…
We discuss how to reconstruct quantum theory from operational postulates. In particular, the following postulates are consistent only with for classical probability theory and quantum theory. Logical Sharpness: There is a one-to-one map…
Quantized compressive sensing (QCS) deals with the problem of representing compressive signal measurements with finite precision representation, i.e., a mandatory process in any practical sensor design. To characterize the signal…
Using Bayes's theorem, we derive a unit-wise recurrence as well as a backward recursion similar to the forward-backward algorithm. The resulting Bayesian recurrent units can be integrated as recurrent neural networks within deep learning…
Bayesian hypothesis testing is re-examined from the perspective of an a priori assessment of the test statistic distribution under the alternative. By assessing the distribution of an observable test statistic, rather than prior parameter…
Given a probability density $P({\bf x}|{\boldsymbol \lambda})$, where $\bf x$ represents continuous degrees of freedom and $\lambda$ a set of parameters, it is possible to construct a general identity relating expectations of observable…
With a Bayesian approach, the linear optics correction algorithm for storage rings is revisited. Starting from the Bayes' theorem, a complete linear optics model is simplified as "likelihood functions" and "prior probability distributions".…
The nonnegativity of the density operator of a state is faithfully coded in its Wigner distribution, and this places constraints on the moments of the Wigner distribution. These constraints are presented in a canonically invariant form…
The classical de Finetti theorem provides an operational definition of the concept of an unknown probability in Bayesian probability theory, where probabilities are taken to be degrees of belief instead of objective states of nature. In…
A nonparametric Bayesian approach is developed to determine quantum potentials from empirical data for quantum systems at finite temperature. The approach combines the likelihood model of quantum mechanics with a priori information over…
The relation between quantum measurement and thermodynamically irreversible processes is investigated. The reduction of the state vector is fundamentally asymmetric in time and shows an observer-relatedness which may explain the double…
In the Jaynes-Cummings model a two-level atom interacts with a single-mode electromagnetic field. Quantum mechanics predicts collapses and revivals in the probability that a measurement will show the atom to be excited at various times…
We present a general formalism for charecterizing 2-time quantum states, describing pre- and post-selected quantum systems. The most general 2-time state is characterized by a `density vector' that is independent of measurements performed…
A phenomenological model for the calculation of reduction probabilities of a superposition of several states is presented. The approach bases only the idea that quantum state reduction has its origin in a mutual physical interaction between…
Reduction is shown to be a possible consequence of the basic principles of quantum mechanics, involving no branching of the quantum state of the universe. The key feature of a measurement is attributed to the creation of macroscopic germs…
We establish a general semiparametric Bernstein-von Mises theorem for Bayesian nonparametric priors based on continuous observations in a periodic reversible multidimensional diffusion model. We consider a wide range of functionals…
A quantum state contains the maximal amount of information available for a given quantum system. In this paper we use weak-value expressions to reconstruct quantum states of continuous-variable systems in the quantum optical domain. The…