Related papers: Constrained quantization for the Cantor distributi…
Shared entanglement can significantly amplify classical correlations between systems interacting over a limited quantum channel. A natural avenue is to use entanglement of the same dimension as the channel because this allows for unitary…
To address the high communication costs of distributed machine learning, a large body of work has been devoted in recent years to designing various compression strategies, such as sparsification and quantization, and optimization algorithms…
We establish some limit theorems for quasi-arithmetic means of random variables. This class of means contains the arithmetic, geometric and harmonic means. Our feature is that the generators of quasi-arithmetic means are allowed to be…
Determining the physical Hilbert space is often considered the most difficult but crucial part of completing the quantization of a constrained system. In such a situation it can be more economical to use effective constraint methods, which…
We study the impact of quantum computation on the fundamental problem of testing the property of distributions. In particular, we focus on testing whether two unknown classical distributions are close or far enough, and propose the…
Quantum systems may contain underlying correlations which are inaccessible to computationally bounded observers. We capture this distinction through a framework that analyses bipartite states only using efficiently implementable quantum…
We study the canonical quantization of a bosonic string in presence of N twist fields. This generalizes the quantization of the twisted string in two ways: the in and out states are not necessarily twisted and the number of twist fields N…
A new five-parameter continuous distribution which generalizes the Kumaraswamy and the beta distributions as well as some other well-known distributions is proposed and studied. The model has as special cases new four- and three-parameter…
The posterior distribution of the number of components k in a finite mixture satisfies a set of inequality constraints. The result holds irrespective of the parametric form of the mixture components and under assumptions on the prior…
Bounds consistency is usually enforced on continuous constraints by first decomposing them into binary and ternary primitives. This decomposition has long been shown to drastically slow down the computation of solutions. To tackle this,…
We define several notions of a limit point on sequences with domain a barrier in $[\omega]^{<\omega}$ focusing on the two dimensional case $[\omega]^2$. By exploring some natural candidates, we show that countable compactness has a number…
We consider the problem of learned transform compression where we learn both, the transform as well as the probability distribution over the discrete codes. We utilize a soft relaxation of the quantization operation to allow for…
Cosmological fine-tuning has traditionally been associated with the narrowness of the intervals in which the parameters of the physical models must be located to make life possible. A more thorough approach focuses on the probability of the…
We initiate the study of constraint satisfaction problems (CSPs) in the presence of counting quantifiers, which may be seen as variants of CSPs in the mould of quantified CSPs (QCSPs). We show that a single counting quantifier strictly…
The quantum fluctuations of a physical property can be observed in the measurement statistics of any measurement that is at least partially sensitive to that physical property. Quantum theory indicates that the effective distribution of…
The ideas of the constraint-based statistics are introduced. The axiom and six theorems of the constraint-based statistics are established.
Quantization provides a very natural way to preserve the convex order when approximating two ordered probability measures by two finitely supported ones. Indeed, when the convex order dominating original probability measure is compactly…
In the setting of a Gaussian channel without power constraints, proposed by Poltyrev, the codewords are points in an n-dimensional Euclidean space (an infinite constellation) and the tradeoff between their density and the error probability…
If only limited control over a multiparticle quantum system is available, a viable method to characterize correlations is to perform random measurements and consider the moments of the resulting probability distribution. We present…
A realistic Quantum Key Distribution (QKD) protocol necessarily deals with finite resources, such as the number of signals exchanged by the two parties. We derive a bound on the secret key rate which is expressed as an optimization problem…