Related papers: Maximal inequalities in quantum probability spaces
In this expository paper, we discuss some of the main geometric inequalities for minimal hypersurfaces. These include the classical monotonicity formula, the Alexander-Osserman conjecture, the isoperimetric inequality for minimal surfaces,…
Von Neumann projections are the main operations by which information can be extracted from the quantum to the classical realm. They are however static processes that do not adapt to the states they measure. Advances in the field of adaptive…
We study the sum uncertainty relations based on variance and skew information for arbitrary finite N quantum mechanical observables. We derive new uncertainty inequalities which improve the exiting results about the related uncertainty…
The role of impossibilities in theories of Physics is mentioned and a recent result is recalled in which Quantum Mechanics is characterized by three information-theoretic impossibilities. The inconvenience of the asymmetries established by…
In quantum computing, knowing the symmetries a given system or state obeys or disobeys is often useful. For example, Hamiltonian symmetries may limit allowed state transitions or simplify learning parameters in machine learning…
Quantum mechanical uncertainty relations for position and momentum are expressed in the form of inequalities involving the Renyi entropies. The proof of these inequalities requires the use of the exact expression for the (p,q)-norm of the…
Maximum-likelihood estimation is applied to identification of an unknown quantum mechanical process represented by a ``black box''. In contrast to linear reconstruction schemes the proposed approach always yields physically sensible…
We prove invariance theorems for general inequalities of different metrics and apply them to limit relations between the sharp constants in the multivariate Markov-Bernstein-Nikolskii type inequalities with the polyharmonic operator for…
We show various sharp Hardy-type inequalities for the linear and quasi-linear Laplacian on non-compact harmonic manifolds with a particular focus on the case of Damek-Ricci spaces. Our methods make use of the optimality theory developed by…
Entropic uncertainty relations play a fundamental role in quantum information theory. However, determining optimal (tight) entropic uncertainty relations for general observables remains a formidable challenge and has so far been achieved…
Wigner's marginal probability theory is revisited, and systematically applied to n-particle correlation measurements. A set of Bell inequalities whose corollaries are Hardy contradiction and its generalisation are derived with intuitive…
Optimal uncertainty quantification (OUQ) is a framework for numerical extreme-case analysis of stochastic systems with imperfect knowledge of the underlying probability distribution. This paper presents sufficient conditions under which an…
We introduce a new class of Frank-Wolfe algorithms for minimizing differentiable functionals over probability measures. This framework can be shown to encompass a diverse range of tasks in areas such as artificial intelligence,…
Under which conditions do outcome probabilities of measurements possess a quantum-mechanical model? This kind of problem is solved here for the case of two dichotomic von Neumann measurements which can be applied repeatedly to a quantum…
The mathematics of classical probability theory was subsumed into classical measure theory by Kolmogorov in 1933. Quantum theory as nonclassical probability theory was incorporated into the beginnings of noncommutative measure theory by von…
When three or more particles are considered, quantum correlations can be stronger than the correlations generated by so-called hybrid local hidden variable models, where some of the particles are considered as a single block inside which…
Bipartite quantum entangled systems can exhibit measurement correlations that violate Bell inequalities, revealing the profoundly counter-intuitive nature of the physical universe. These correlations reflect the impossibility of…
Small corrections to the uncertainty relations, with effects in the ultraviolet and/or infrared, have been discussed in the context of string theory and quantum gravity. Such corrections lead to small but finite minimal uncertainties in…
We derive a family of inequalities involving different phase-space distributions of a quantum state which have to be fulfilled by any classical state. The violation of these inequalities is a clear signature of nonclassicality. Our approach…
A hereditarily atomic von Neumann algebra $A$ is a $W^*$ product of matrix algebras, regarded as the underlying function algebra of a quantum set. Projections in $A\overline{\otimes}A^{\circ}$ are interpreted as quantum binary relations on…