Related papers: Finite de Finetti theorem for conditional probabil…
General methods of quantitative and qualitative continuity analysis of characteristics of composite quantum systems are described. Several modifications of the Alicki-Fannes-Winter method are considered, which make it applicable to a wide…
Sharp, nonasymptotic bounds are obtained for the relative entropy between the distributions of sampling with and without replacement from an urn with balls of $c\geq 2$ colors. Our bounds are asymptotically tight in certain regimes and,…
Let Alice and Bob be able to make local quantum measurements and communicate classically. The set of mathematically consistent joint probability assignments (``states'') for such measurements is properly larger than the set of…
General Probabilistic Theories provide the most general mathematical framework for the theory of probability in an operationally natural manner, and generalize classical and quantum theories. In this article, we study state-discrimination…
The Shapley-Folkman theorem shows that Minkowski averages of uniformly bounded sets tend to be convex when the number of terms in the sum becomes much larger than the ambient dimension. In optimization, Aubin and Ekeland [1976] show that…
It is possible to completely explain all aspects of quantum mechanics by expressing the relations between physical properties in terms of complex conditional probabilities (Phys. Rev. A 89, 042115(2014)). These fully deterministic…
Let $q \in (0,1)$. We formulate an asymptotic version of the $q$-analogue of de Finetti's theorem. Using the convex structure of the space of $q$-exchangeable probability measures, we show that the optimal rate of convergence is of order…
We show that the linearity of an evolution of Quantum Mechanics follows from the definition of kinematics. The same result is obtained for an arbitrary theory with the state space that includes mixtures of different preparations. Next, we…
We show that, assuming that quantum mechanics holds locally, the finite speed of information is the principle that limits all possible correlations between distant parties to be quantum mechanical as well. Local quantum mechanics means that…
This work discusses simple examples how quantum systems are obtained as subsystems of classical statistical systems. For a single qubit with arbitrary Hamiltonian and for the quantum particle in a harmonic potential we provide explicitly…
An approximate analytical scheme of the dynamical mean field theory (DMFT) is developed for the description of the electron (ion) lattice systems with Hubbard correlations within the asymmetric Hubbard model where the chemical potentials…
We study how the spin-statistics theorem relates to the geometric structures on phase space that are introduced in quantisation procedures (namely a U(1) bundle and connection). The relation can be proved in both the relativistic and the…
We study the convergence of the empirical distribution associated with a system of interacting kinetic particles subject to independent Brownian forcing in a finite horizon setting, using some recent progress on kinetic non-linear partial…
The bipartite entanglement of a pure quantum state is known to be characterized by its Schmidt decomposition. In particular the state is maximally entangled when all the Schmidt coefficients are equal. We point out a convenient method which…
Starting from the guiding principles of spacetime locality and operationalism, a general framework for a probabilistic description of nature is proposed. Crucially, no notion of time or metric is assumed, neither any specific physical…
We investigate the occurrence of additive and multiplicative structures in random subsets of the natural numbers. Specifically, for a Bernoulli random subset of $\mathbb{N}$ where each integer is included independently with probability…
We prove that all deterministic hidden-variables theories, that reproduce quantum theory for a 'quantum equilibrium' distribution of hidden variables, predict the existence of instantaneous signals at the statistical level for hypothetical…
A central limit theorem is established for a sum of random variables belonging to a sequence of random fields. The fields are assumed to have zero mean conditional on the past history and to satisfy certain conditional $\alpha$-mixing…
We introduce a new framework for contextuality based on simplicial sets, combinatorial models of topological spaces that play a prominent role in modern homotopy theory. Our approach extends measurement scenarios to consist of spaces…
What singles out quantum mechanics as the fundamental theory of Nature? Here we study local measurements in generalised probabilistic theories (GPTs) and investigate how observational limitations affect the production of correlations. We…