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The Wigner's friend thought experiment has gained a resurgence of interest in recent years thanks to no-go theorems that extend it to Bell-like scenarios. One of these, by us and co-workers, showcased the contradiction that arises between…
Locality of interactions is an essential ingredient of Special Relativity. Recently, a new framework under the name of relative locality \cite{AmelinoCamelia:2011bm} has been proposed as a way to consider Planckian modifications of the…
The unique entanglement measure is concurrence in a 2-qubit pure state. The maximum violation of Bell's inequality is monotonically increasing for this quantity. Therefore, people expect that pure state entanglement is relevant to the…
It is by now well-recognised that the na\"ive application of the projection postulate on composite quantum systems can induce signalling between their constituent components, indicative of a breakdown of causality in a relativistic…
We give a necessary and sufficient condition on a compact semitopological quantum semigroup which turns it into a compact quantum group. In particular, we obtain a generalisation of Ellis's joint continuity theorem. We also investigate the…
Mukhin found in 1984 an important necessary and sufficient condition for the validity of the local limit theorem. Revisiting the succint proof given in \cite{Mu2}, we could only prove rigorously a weaker necessary and sufficient condition,…
We correct a condition in a result of Johnson and Samworth (Bernoulli 11 (2005) 829--845) concerning convergence to stable laws in Mallows distance. We also give an improved version of this result, setting it in the more familiar context of…
The notion coexistence of quantum observables was introduced to describe the possibility of measuring two or more observables together. Here we survey the various different formalisations of this notion and their connections. We review…
The non-local correlations exhibited when measuring entangled particles can be used to certify the presence of genuine randomness in Bell experiments. While non-locality is necessary for randomness certification, it is unclear when and why…
The changes that quantum states undergo during measurement are both probabilistic and nonlocal. These two characteristics complement one another to insure compatibility with relativity and maintain conservation laws. The probabilistic…
We announce three results in the theory of Jacobi matrices and Schr\"odinger operators. First, we give necessary and sufficient conditions for a measure to be the spectral measure of a Schr\"odinger operator $-\f{d^2}{dx^2} +V(x)$ on $L^2…
The proof of the Heisenberg uncertainty relation is modified to produce two improvements: (a) the resulting inequality is stronger because it includes the covariance between the two observables, and (b) the proof lifts certain restrictions…
We review old and recent finite de Finetti theorems in total variation distance and in relative entropy, and we highlight their connections with bounds on the difference between sampling with and without replacement. We also establish two…
In this paper, the defining properties of a valid measure of the dependence between two random variables are reviewed and complemented with two original ones, shown to be more fundamental than other usual postulates. While other popular…
A simple proof of a key inequality required by the paper's analysis is presented. An introductory section discussing the paper's setup may be helpful to some readers. An alternative statistical analysis is suggested.
The incompatibility of the measurements constraints the achievable precisions in multi-parameter quantum estimation. Understanding the tradeoff induced by such incompatibility is a central topic in quantum metrology. Here we provide an…
I impose previously neglected symmetry conditions in Leggett's non-local hidden variable theory that are required by the conditions in a recent experimental test of this theory. These conditions lead to an inequality for the polarization…
We establish new results of first-order necessary conditions of optimality for finite-dimensional problems with inequality constraints and for problems with equality and inequality constraints, in the form of John's theorem and in the form…
We present a way of experimentally determining the concurrence in terms of the expectation values of local observables for arbitrary multipartite pure states. In stead of the joint measurements on two copies of a state in the experiment for…
A popular current research trend deals with expanding the Monte-Carlo tree search sampling methodologies to the environments with uncertainty and incomplete information. Recently a finite population version of Geiringer theorem with…