Related papers: Kolmogorov complexity and the asymptotic bound for…
We prove that a random linear code over F_q, with probability arbitrarily close to 1, is list decodable at radius (1-1/q-\epsilon) with list size L=O(1/\epsilon^2) and rate R=\Omega_q(\epsilon^2/(log^3(1/\epsilon))). Up to the…
We consider a non-uniformly elliptic second-order differential operator with periodic coefficients that models composite media consisting of highly anisotropic cylindrical fibres periodically distributed in an isotropic background. The…
Motivated by the statistical analysis of the discrete optimal transport problem, we prove distributional limits for the solutions of linear programs with random constraints. Such limits were first obtained by Klatt, Munk, & Zemel (2022),…
We prove a very general lower bound technique for quantum and randomized query complexity, that is easy to prove as well as to apply. To achieve this, we introduce the use of Kolmogorov complexity to query complexity. Our technique…
The concept of asymptotic correctability of Bell-diagonal quantum states is generalised to elementary quantum systems of higher dimensions. Based on these results basic properties of quantum state purification protocols are investigated…
This paper is devoted to the study of the asymptotic behavior of solutions to multi-order fractional cooperative systems. First, we demonstrate the boundedness of solutions to fractional-order systems under certain conditions imposed on the…
We show that a quantum architecture with an error correction procedure limited to geometrically local operations incurs an overhead that grows with the system size, even if arbitrary error-free classical computation is allowed. In…
The asymptotic dimension of metric spaces is an important notion in geometric group theory introduced by Gromov. The metric spaces considered in this paper are the ones whose underlying spaces are the vertex-sets of graphs and whose metrics…
We derive an asymptotic lower bound on the Bayes risk when N identical quantum systems whose state depends on a vector of unknown parameters are jointly measured in an arbitrary way and the parameters of interest estimated on the basis of…
We exhibit a simple, systematic procedure for detecting and correcting errors using any of the recently reported quantum error-correcting codes. The procedure is shown explicitly for a code in which one qubit is mapped into five. The…
Estimates of the quantum accuracy threshold often tacitly assume that it is possible to interact arbitrary pairs of qubits in a quantum computer with a failure rate that is independent of the distance between them. None of the many physical…
Quantum computation is a subject of much theoretical promise, but has not been realized in large scale, despite the discovery of fault-tolerant procedures to overcome decoherence. Part of the reason is that the theoretically modest…
This paper presents a new derivation method of converse bounds on the non-asymptotic achievable rate of discrete weakly symmetric memoryless channels. It is based on the finite blocklength statistics of the channel, where with the use of an…
We present an asymptotic formula for the number of line segments connecting q+1 points of an nxn square grid, and a sharper formula, assuming the Riemann hypothesis. We also present asymptotic formulas for the number of lines through at…
We study dynamical decoupling in a multi-qubit setting, where it is combined with quantum logic gates. This is illustrated in terms of computation using Heisenberg interactions only, where global decoupling pulses commute with the…
A family of quantum codes of increasing block length with positive rate is asymptotically good if the ratio of its distance to its block length approaches a positive constant. The asymptotic quantum Gilbert-Varshamov (GV) bound states that…
Estimation of quantum relative entropy and its R\'{e}nyi generalizations is a fundamental statistical task in quantum information theory, physics, and beyond. While several estimators of these divergences have been proposed in the…
Recently Shor showed how to perform fault tolerant quantum computation when the error probability is logarithmically small. We improve this bound and describe fault tolerant quantum computation when the error probability is smaller than…
Recently, the present authors derived new asymptotic expansions for linear differential equations having a simple turning point. These involve Airy functions and slowly varying coefficient functions, and were simpler than previous…
The need for recognition/approximation of functions in terms of elementary functions/operations emerges in many areas of experimental mathematics, numerical analysis, computer algebra systems, model building, machine learning, approximation…