Related papers: Uniform continuity of POVMs
A Positive Operator Valued Measure (POVM) is a map $F:\mathcal{B}(X)\to\mathcal{L}_s^+(\mathcal{H})$ from the Borel $\sigma$-algebra of a topological space $X$ to the space of positive self-adjoint operators on a Hilbert space…
A hidden Markov model is called observable if distinct initial laws give rise to distinct laws of the observation process. Observability implies stability of the nonlinear filter when the signal process is tight, but this need not be the…
We prove a theorem about positive-operator-valued measures (POVMs) that is an analog of the Kolmogorov extension theorem, a standard theorem of probability theory. According to our theorem, if a sequence of POVMs G_n on $\mathbb{R}^n$…
A normalized positive operator measure $X\mapsto E(X)$ has the norm-1-property if $\no{E(X)}=1$ whenever $E(X)\ne O$. This property reflects the fact that the measurement outcome probabilities for the values of such observables can be made…
Permanental sequences with non-symmetric kernels that are generalization of the potentials of a Markov chain with state space $\{0,1/2, \ldots, 1/n,\ldots\}$ that was introduced by Kolmogorov, are studied. Depending on a parameter in the…
This paper studies transition probabilities from a Borel subset of a Polish space to a product of two Borel subsets of Polish spaces. For such transition probabilities it introduces and studies the property of semi-uniform Feller…
Using a recent result of Albini et al. to represent quantum homodyne tomography in terms of a single observable (as a normalized positive operator measure) we construct a generalized Markov kernel which transforms (the measurement outcome…
We study existence and uniqueness of invariant probability measures for continuous-time Markov processes on general state spaces. Existence is obtained from tightness of time averages under a weak regularity assumption inspired by…
We give a characterization of commutative semispectral measures by means of Feller and Strong Feller Markov kernels. In particular: {itemize} we show that a semispectral measure $F$ is commutative if and only if there exist a self-adjoint…
The fundamental principles of complementarity and uncertainty are shown to be related to the possibility of joint unsharp measurements of pairs of noncommuting quantum observables. A new joint measurement scheme for complementary…
We study two equivalent characterizations of the strong Feller property for a Markov process and of the associated sub-Markovian semigroup. One is described in terms of locally uniform absolute continuity, whereas the other uses local…
Superposition is an essential feature of quantum mechanics. From the Schrodinger's cat to quantum algorithms such as Deutsch-Jorsza algorithm, quantum superposition plays an important role. It is one fundamental and crucial question how to…
We consider Hidden Markov Models that emit sequences of observations that are drawn from continuous distributions. For example, such a model may emit a sequence of numbers, each of which is drawn from a uniform distribution, but the support…
We construct a generalized Markov kernel which transforms the observable associated with the homodyne tomography into a covariant phase space observable with a regular kernel state. Illustrative examples are given in the cases of a…
We obtain a formal characterization of the compatibility or otherwise of a set of positive-operator-valued measures (POVMs) via their Naimark extensions. We show that a set of POVMs is jointly measurable if and only if there exists a single…
In this paper, we study the cohomology of vector bundles on projective space defined as kernels or cokernels of general maps $V_1 \to V_2$, where the $V_i$ are direct sums of line bundles or certain exceptional bundles. We prove an…
We further investigate the uniform regularity property of collections of sets via primal and dual characterizing constants. These constants play an important role in determining convergence rates of projection algorithms for solving…
We review various unitary network models used in quantum computing, spectral analysis or condensed matter physics and establish relationships between them. We show that symmetric one dimensional quantum walks are universal, as are CMV…
We detail and extend the results of [Milman {\it et al.}, Phys. Rev. Lett. {\bf 99}, 130405 (2007)] on Bell-type inequalities based on correlations between measurements of continuous observables performed on trapped molecular systems. We…
We provide a characterisation of the continuous-time Markov models where the Markov matrices from the model can be parameterised directly in terms of the associated rate matrices (generators). That is, each Markov matrix can be expressed as…