相关论文: Optimal quantization for some triadic uniform Cant…

For the four-state protocol of quantum key distribution, optimum sets of probe parameters are calculated for the most general unitary probe in which each individual transmitted photon is made to interact with the probe so that the signal…

We propose new optimal estimators for the Lipschitz frontier of a set of points. They are defined as kernel estimators being sufficiently regular, covering all the points and whose associated support is of smallest surface. The estimators…

We study the maximum $k$-set coverage problem in the following distributed setting. A collection of sets $S_1,\ldots,S_m$ over a universe $[n]$ is partitioned across $p$ machines and the goal is to find $k$ sets whose union covers the most…

We consider the problem of discrimination between two pure quantum states. It is well known that the optimal measurement under both the error-probability and log-loss criteria is a projection, while under an ``erasure-distortion'' criterion…

In this paper we explore fundamental problems in randomized communication complexity such as computing Set Intersection on sets of size $k$ and Equality Testing between vectors of length $k$. Sa\u{g}lam and Tardos and Brody et al. showed…

A certain spectrum, indexed by a\in[0,\infty], of upper bounds P_a(X;x) on the tail probability P(X\geq x), with P_0(X;x)=P(X\geq x) and P_\infty(X;x) being the best possible exponential upper bound on P(X\geq x), is shown to be stable and…

The canonical polyadic decomposition (CPD) of a low rank tensor plays a major role in data analysis and signal processing by allowing for unique recovery of underlying factors. However, it is well known that the low rank CPD approximation…

We derive an optimal bound on the sum of entropic uncertainties of two or more observables when they are sequentially measured on the same ensemble of systems. This optimal bound is shown to be greater than or equal to the bounds derived in…

In this paper, we examine the optimal quantization of signals for system identification. We deal with memoryless quantization for the output signals and derive the optimal quantization schemes. The objective functions are the errors of…

The Knill-Laflamme (KL) conditions distinguish exact quantum error correction codes, and it has played a critical role in the discovery of state-of-the-art codes. However, the family of exact codes is a very restrictive one and does not…

In this paper, we study an asymptotic approximation of the Fisher information for the estimation of a scalar parameter using quantized measurements. We show that, as the number of quantization intervals tends to infinity, the loss of Fisher…

A regularization algorithm allowing random noise in derivatives and inexact function values is proposed for computing approximate local critical points of any order for smooth unconstrained optimization problems. For an objective function…

We propose a novel optimization scheme designed to find optimally correctable subspace codes for a known quantum noise channel. To each candidate subspace code we first associate a universal recovery map, as if the code was perfectly…

For any positive integer $p\geq 3$, let $A$ be a proper subset of $\{0,1,\ldots, p-1\}$ with $\sharp A=s\geq 2$. Suppose $h: \{0,1,\ldots,s-1\}\to A$ is a one-to-one map which is strictly increasing with $A=\{h(0),h(1),\ldots,h(s-1)\}$. We…

In many quantization problems, the distortion function is given by the Euclidean metric to measure the distance of a source sample to any given reproduction point of the quantizer. We will in this work regard distortion functions, which are…

The problem of designing optimal quantization rules for sequential detectors is investigated. First, it is shown that this task can be solved within the general framework of active sequential detection. Using this approach, the optimal…

This paper discusses an alternative to conditioning that may be used when the probability distribution is not fully specified. It does not require any assumptions (such as CAR: coarsening at random) on the unknown distribution. The…

Let $X_1,\dots,X_n$ be i.i.d. log-concave random vectors in $\mathbb R^d$ with mean 0 and covariance matrix $\Sigma$. We study the problem of quantifying the normal approximation error for $W=n^{-1/2}\sum_{i=1}^nX_i$ with explicit…

Extending results of Linial (1984) and Aigner (1985), we prove a uniform lower bound on the balance constant of a poset $P$ of width $2$. This constant is defined as $\delta(P) = \max_{(x, y)\in P^2}\min\{\mathbb{P}(x\prec y),…

Three-point semidefinite programming bounds are one of the most powerful known tools for bounding the size of spherical codes. In this paper, we use them to prove lower bounds for the potential energy of particles interacting via a pair…