Related papers: Generalised Pinching Inequality
Quantum measurements with feed-forward are crucial components of fault-tolerant quantum computers. We show how the error rate of such a measurement can be directly estimated by fitting the probability that successive randomly compiled…
It is well known that general variational inequalities provide us with a unified, natural, novel and simple framework to study a wide class of unrelated problems, which arise in pure and applied sciences. In this paper, we present a number…
Minwise hashing (Minhash) is a widely popular indexing scheme in practice. Minhash is designed for estimating set resemblance and is known to be suboptimal in many applications where the desired measure is set overlap (i.e., inner product…
Measurements are a vital part of any quantum computation, whether as a final step to retrieve results, as an intermediate step to inform subsequent operations, or as part of the computation itself (as in measurement-based quantum…
Pisier's inequality is central in the study of normed spaces and has important applications in geometry. We provide an elementary proof of this inequality, which avoids some non-constructive steps from previous proofs. Our goal is to make…
We establish variant Khintchine inequalities on normed spaces of Hanner type and cotype, in which the Rademacher distribution corresponding to classical Khintchine inequality is replaced by general symmetric distributions. The proof…
We introduce a framework for simulating quantum measurements based on classical processing of a set of accessible measurements. Well-known concepts such as joint measurability and projective simulability naturally emerge as particular cases…
The statistical measure of spatial inhomogeneity for n points placed in chi cells each of size kxk is generalized to incorporate finite size objects like black pixels for binary patterns of size LxL. As a function of length scale k, the…
We offer a new proof of uniform convexity inequalities for the Finsler manifold of nonpositive curvature taken on the space of positive-semidefinite matrices with the weighted matrix geometric mean defining the geodesic between two points.…
We solve the problem of best approximation by partial isometries of given rank to an arbitrary rectangular matrix, when the distance is measured in any unitarily invariant norm. In the case where the norm is strictly convex, we parametrize…
A large literature has grown up around the proposed use of 'weak measurements' (i.e., unsharp measurements followed by post-selection) to allegedly provide information about hidden ontological features of quantum systems. This paper…
Metric projection operators can be defined in similar wayin Hilbert and Banach spaces. At the same time, they differ signifitiantly in their properties. Metric projection operator in Hilbert space is a monotone and nonexpansive operator. It…
A generalization of the Bernstein matrix concentration inequality to random tensors of general order is proposed. This generalization is based on the use of Einstein products between tensors, from which a strong link can be established…
Matching is a widely used causal inference design that aims to approximate a randomized experiment using observational data by forming matched sets of treated and control units based on similarities in their covariates. Ideally, treated…
Partial differential equations are central to describing many physical phenomena. In many applications these phenomena are observed through a sensor network, with the aim of inferring their underlying properties. Leveraging from certain…
We develop some theoretical results for a robust similarity measure named "generalized min-max" (GMM). This similarity has direct applications in machine learning as a positive definite kernel and can be efficiently computed via…
Many major works in social science employ matching to make causal conclusions, but different matches on the same data may produce different treatment effect estimates, even when they achieve similar balance or minimize the same loss…
The uncertainty principle bounds the uncertainties about incompatible measurements, clearly setting quantum theory apart from the classical world. Its mathematical formulation via uncertainty relations, plays an irreplaceable role in…
We quantify the intrinsic noise content of an observable in a general probabilistic theory and derive a noise content inequality for incompatible observables. We apply the derived inequality to standard quantum theory, the quantum theory of…
It is a key issue to characterize the model of standard quantum theory out of general models by an operational condition. The framework of General Probabilistic Theories (GPTs) is a new information theoretical approach to single out…