Related papers: Two Proofs of Fine's Theorem

For the case of two spin-1/2 particles in the singlet state, we provide a GHZ-type proof of Bell's theorem by using the idea of postselected measurements. Furthermore, we show that in spite of the low efficiency of the detectors one can…

We analyse the complexity of approximate counting constraint satisfactions problems $\mathrm{\#CSP}(\mathcal{F})$, where $\mathcal{F}$ is a set of nonnegative rational-valued functions of Boolean variables. A complete classification is…

Maximum likelihood fits to data can be done using binned data (histograms) and unbinned data. With binned data, one gets not only the fitted parameters but also a measure of the goodness of fit. With unbinned data, currently, the fitted…

A conceptually simpler proof of the separability criterion for two-qubit systems, which is referred to as "Hefei inequality" in literature, is presented. This inequality gives a necessary and sufficient separability criterion for any mixed…

We adopt an empirical approach to the characterization of the distribution of twin primes within the set of primes, rather than in the set of all natural numbers. The occurrences of twin primes in any finite sequence of primes are like…

We develop a framework for the operationalization of models and parameters by combining de Finetti's representation theorem with a conditional form of Sanov's theorem. This synthesis, the tilted de Finetti theorem, shows that conditioning…

The many-normal-means problem is a classic example that motivates the development of many important inferential procedures in the history of statistics. In this short note, we consider a further special case of the problem, which involves…

This paper deals with the existence and uniqueness of solutions to kinetic equations describing alignment of self-propelled particles. The particularity of these models is that the velocity variable is not on the euclidean space but…

Under the null hypothesis, the marginal probability of the positive response is symmetric at any specified correlated coefficient, and the discordance probability is also symmetric to the positive response probability. The marginal…

It was shown in [Augusiak et al.,\;Phys. Rev. A \textbf{77}, 030301(R) (2008)] that discrimination between entanglement and separability in a two qubit state can be achieved by a measurement of a single observable on four copies of it.…

Many protocols of quantum information processing use entangled states. Hence, separability criteria are of great importance. We propose new separability conditions for a bipartite finite-dimensional system. They are derived by using…

We analyze and compare the mathematical formulations of the criterion for separability for bipartite density matrices and the Bell inequalities. We show that a violation of a Bell inequality can formally be expressed as a witness for…

Violation of Bell's Inequalities gives experimental evidence for the existence of a spin 1/2 which has two simultaneous axes of spin quantization rather than one. These couple to form a resonance state, called the spin fringe, and this…

A simple local hidden-variables model is exhibited which reproduces the results of all performed tests of Bell\'{}s inequalities involving optical photon pairs. For the old atomic-cascade experiments, like Aspect\'{}s, the model agrees with…

The entanglement phenomenon on example of Smolin state of four qubits is discussed. This state is known as bound entangled state and the spin tomogram of the state is found in explicit form. The qubit portrait method is used the Bell…

Well known Simpson's paradox is puzzling and surprising for many, especially for the empirical researchers and users of statistics. However there is no surprise as far as mathematical details are concerned. A lot more is written about the…

We study optimization problems in which a linear functional is maximized over probability measures that are dominated by a given measure according to an integral stochastic order in an arbitrary dimension. We show that the following four…

We analyze optical EPR experimental data performed by Weihs et al in Innsbruck 1997-1998. We show that for some linear combinations of the raw coincidence rates, the experimental results display some anomalous behavior that a more general…

We study a hypothesis testing problem in which data is compressed distributively and sent to a detector that seeks to decide between two possible distributions for the data. The aim is to characterize all achievable encoding rates and…

The paper presents new sufficient conditions for the property of strong bi-metric regularity of the optimality map associated with an optimal control problem which is affine with respect to the control variable ({\em affine problem}). The…