Related papers: Sufficient conditions for some transform orders ba…

We generalize the concept of population for non-Hermitian systems in different ways and identify the one best suited to characterize adiabaticity. An approximate adiabaticity criterion consistent with this choice is also worked out.…

We introduce a notion of contextuality for transformations in sequential contexts, distinct from the Bell-Kochen-Specker and Spekkens notions of contextuality. Within a transformation-based model for quantum computation we show that strong…

Symmetries and their anomalies are powerful tools for understanding quantum systems. However, realistic systems are often subject to disorders, dissipation and decoherence. In many circumstances, symmetries are not exact but only on…

Theoretical results for importance sampling rely on the existence of certain moments of the importance weights, which are the ratios between the proposal and target densities. In particular, a finite variance ensures square root convergence…

For a general nonlinear control system, we study the problem of small time local attainability of a target which is the closure of an open set. When the target is smooth and locally the sublevel set of a smooth function, we develop second…

Based on the standard transfer matrix, a formally exact quantization condition for arbitrary potentials, which outflanks and unifies the historical approaches, is derived. It can be used to find the exact bound-state energy eigenvalues of…

The difficulty in manipulating quantum resources deterministically often necessitates the use of probabilistic protocols, but the characterization of their capabilities and limitations has been lacking. We develop a general approach to this…

We consider random systems of equations x_1 + ... + x_k = a; 0 <= a <= 2 which are interpreted as equations modulo 3: We show for k >= 15 that the satisfiability threshold of such systems occurs where the 2-core has density 1: We show a…

We show that a family of random variables is uniformly integrable if and only if it is stochastically bounded in the increasing convex order by an integrable random variable. This result is complemented by proving analogous statements for…

We consider a non-autonomous ordinary differential equation on a smooth manifold, with right-hand side that randomly switches between the elements of a finite family of smooth vector fields. For the resulting random dynamical system, we…

We propose for the spin density matrix two parametrizations which automatically fulfil the non-negativity conditions, without setting any bound on the parameters. The first one relies on a theorem, that we prove, and it is rather simple and…

Shape constrained densities are encountered in many nonparametric estimation problems. The classes of monotone or convex (and monotone) densities can be viewed as special cases of the classes of k-monotone densities. A density g is said to…

We consider the problem of counting $k$-tuples of positive integers satisfying any arbitrary set of gcd conditions, where every integer is not larger than $x$. We first establish the conditions to guarantee the existence of such tuples, and…

We introduce a comprehensive method for establishing stochastic orders among order statistics in the i.i.d. case. This approach relies on the assumption that the underlying distribution is linked to a reference distribution through a…

We establish necessary and sufficient conditions for the N-representability of the universal one-electron reduced density matrix functional. Functionals satisfying these conditions are guaranteed to yield variational upper bounds on the…

We derive a hierarchy of continuous-variable multipartite entanglement conditions in terms of second-order moments of position and momentum operators that generalizes existing criteria. Each condition corresponds to a convex optimization…

Quantum entanglement is known to be monogamous, i.e., it obeys strong constraints on how the entanglement can be distributed among multipartite systems. Almost all the entanglement monotones so far are shown to be monogamous. We explore…

We propose a general framework for solving quantum state estimation problems using the minimum relative entropy criterion. A convex optimization approach allows us to decide the feasibility of the problem given the data and, whenever…

We consider a simple model for active random walk with general temporal correlations, and investigate the shape of the probability distribution function of the displacement during a short time interval. We find that under certain conditions…

We study asymptotic state transformations in continuous variable quantum resource theories. In particular, we prove that monotones displaying lower semicontinuity and strong superadditivity can be used to bound asymptotic transformation…