Related papers: Robust Optimality of Gaussian Noise Stability
Quantum discord is a measure of non-classical correlations, which are excess correlations inherent in quantum states that cannot be accessed by classical measurements. For multipartite states, the classically accessible correlations can be…
In this article, we consider the stochastic wave equation on $\mathbb{R}_{+} \times \mathbb{R}$, driven by a linear multiplicative space-time homogeneous Gaussian noise whose temporal and spatial covariance structures are given by locally…
We establish well-posedness in the mild sense for a class of stochastic semilinear evolution equations with a polynomially growing quasi-monotone nonlinearity and multiplicative Poisson noise. We also study existence and uniqueness of…
Some quantum measurements can not be performed simultaneously, i.e. they are incompatible. Here we show that every set of incompatible measurements provides an advantage over compatible ones in a suitably chosen quantum state discrimination…
We study the task of testable learning of general -- not necessarily homogeneous -- halfspaces with adversarial label noise with respect to the Gaussian distribution. In the testable learning framework, the goal is to develop a…
A better understanding of the instability margin will eventually optimize the operational range for safety-critical industries. In this paper, we investigate the almost-sure exponential asymptotic stability of the trivial solution of a…
This paper explores conditions of existence of different types of consistent tests. New links of these types of consistency are also established. The existence of discernible (strong consistent) tests follows from the existence of pointwise…
We study the algorithmic task of testably learning general Massart halfspaces under the Gaussian distribution. In the testable learning setting, the aim is the design of a tester-learner pair satisfying the following properties: (1) if the…
Parameter estimation is of fundamental importance in areas from atomic spectroscopy and atomic clocks to gravitational wave detection. Entangled probes provide a significant precision gain over classical strategies in the absence of noise.…
This paper studies the stability properties of stochastic differential equations subject to persistent noise (including the case of additive noise), which is noise that is present even at the equilibria of the underlying differential…
Quantum chaotic maps can efficiently generate pseudo-random states carrying almost maximal multipartite entanglement, as characterized by the probability distribution of bipartite entanglement between all possible bipartitions of the…
We introduce a stability criterion for quantum statistical ensembles describing macroscopic systems. An ensemble is called "stable" when a small number of local measurements cannot significantly modify the probability distribution of the…
We generalize the stable graph regularity lemma of Malliaris and Shelah to the case of finite structures in finite relational languages, e.g., finite hypergraphs. We show that under the model-theoretic assumption of stability, such a…
We study stability of metric approximations of countable groups with respect to groups endowed with ultrametrics, the main case study being a $p$-adic analogue of Ulam stability, where we take $GL_n(\mathbb{Z}_p)$ as approximating groups…
Stable subgroups and the Morse boundary are two systematic approaches to collect and study the hyperbolic aspects of finitely generated groups. In this paper we unify and generalize these strategies by viewing any geodesic metric space as a…
The structure theorem is established which shows that an arbitrary multi-mode bosonic Gaussian observable can be represented as a combination of four basic cases, the physical prototypes of which are homodyne and heterodyne, noiseless or…
Deterministic chaotic dynamics presumes that the state space can be partitioned arbitrarily finely. In a physical system, the inevitable presence of some noise sets a finite limit to the finest possible resolution that can be attained. Much…
We consider the stability of Robust Optimization problems with respect to perturbations in their uncertainty sets. We focus on Linear Optimization problems, including those with a possibly infinite number of constraints, also known as…
It is difficult to choose detection thresholds for tests of non-stationarity that assume {\em a priori} a noise model if the data is statistically uncharacterized to begin with. This is a potentially serious problem when an automated…
We study the transport properties of the Gaussian measures on Sobolev spaces under the dynamics of the cubic fourth order nonlinear Schr\"odinger equation on the circle. In particular, we establish an optimal regularity result for…