Related papers: Doubling measures on uniform Cantor sets
A universal programmable detector is a device that can be tuned to perform any desired measurement on a given quantum system, by changing the state of an ancilla. With a finite dimension d for the ancilla only approximate universal…
We generalize the method of combinatorial telescoping to the case of multiple summations. We shall demonstrate this idea by giving combinatorial proofs for two identities of Andrews on parity indices of partitions.
We study here a sequence of secondary measures, so called because the set of secondary polynomials on a given term become orthogonal for the next measure. The main result is a formula making explicit the density of any term of the sequence,…
The determination of a quantum observable from the first and second moments of its measurement outcome statistics is investigated. Operational conditions for the moments of a probability measure are given which suffice to determine the…
Mahler's measure defines a dynamical system on the algebraic numbers. In this paper, we study the problem of which number fields have points which wander under the iteration of Mahler's measure. We completely solve the problem for all…
Two-qubit X-matrices have been the subject of considerable recent attention, as they lend themselves more readily to analytical investigations than two-qubit density matrices of arbitrary nature. Here, we maximally exploit this relative…
We introduce the concepts of dual instruments and sub-observables. We show that although a dual instruments measures a unique observable, it determines many sub-observables. We define a unique minimal extension of a sub-observable to an…
We discuss two ways to construct standard probability measures, called push-down measures, from internal probability measures. We show that the Wasserstein distance between an internal probability measure and its push-down measure is…
We establish the analogue of Khintchine's theorem for all self-similar probability measures on the real line. When specified to the case of the Hausdorff measure on the middle-thirds Cantor set, the result is already new and provides an…
In this paper we investigate measures over bounded lattices, extending and giving a unifying treatment to previous works. In particular, we prove that the measures of an arbitrary bounded lattice can be represented as measures over a…
Simultaneous decoherence of conjugate observables of an open quantum system leads to a classical statistical mechanical description with constant phase space probability density in terms of a uniform ensemble. We investigate a scenario…
The problem of defining quantum probabilities of composite events is considered. This problem is of high importance for the theory of quantum measurements and for quantum decision theory that is a part of measurement theory. We show that…
We undertake a comprehensive study of measure equivalence between general locally compact, second countable groups, providing operator algebraic and ergodic theoretic reformulations, and complete the classification of amenable groups within…
We investigate optimal discrimination between two projective quantum measurements on a single qubit. We consider scenario where the measurement that should be identified can be performed twice and we show that adaptive discrimination…
In this paper we continue to explore infinitely renormalizable H\'enon maps with small Jacobian. It was shown in [CLM] that contrary to the one-dimensional intuition, the Cantor attractor of such a map is non-rigid and the conjugacy with…
Quantum measurement is universal for quantum computation. This universality allows alternative schemes to the traditional three-step organisation of quantum computation: initial state preparation, unitary transformation, measurement. In…
Probabilities of the outcomes of consecutive quantum measurements can be obtained by construction probability amplitudes, thus implying unitary evolution of the measured system, broken each time a measurement is made. In practice, the…
A new combinatorial-probabilistic diagnostic entropy has been introduced. It describes the pair-wise sum of probabilities of system conditions that have to be distinguished during the diagnosing process. The proposed measure describes the…
Quantization for a Borel probability measure refers to the idea of estimating a given probability by a discrete probability with support containing a finite number of elements. If in the quantization some of the elements in the support are…
We study distributional similarity measures for the purpose of improving probability estimation for unseen cooccurrences. Our contributions are three-fold: an empirical comparison of a broad range of measures; a classification of similarity…