Related papers: On the asymptotic quantization error for the doubl…
We study the estimation of the overlap between two unknown pure quantum states of a finite dimensional system, given $M$ and $N$ copies of each type. This is a fundamental primitive in quantum information processing that is commonly…
We are interested in proposing approximations of a sequence of probability measures in the convex order by finitely supported probability measures still in the convex order. We propose to alternate transitions according to a martingale…
In hypothesis testing with quantum states, given a black box containing one of the two possible states, measurement is performed to detect in favor of one of the hypotheses. In postselected hypothesis testing, a third outcome is added,…
We describe two procedures which, given access to one copy of a quantum state and a sequence of two-outcome measurements, can distinguish between the case that at least one of the measurements accepts the state with high probability, and…
Let $\mu$ be a doubling measure in $\mathbb{R}^n$. We investigate quantitative relations between the rectifiability of $\mu$ and its distance to flat measures. More precisely, for $x$ in the support $\Sigma$ of $\mu$ and $r > 0$, we…
We characterize two-weight inequalities for certain maximal truncations of the Hilbert transform in terms of testing conditions on simpler functions. For 1<p<2 and two positive Borel measures u, v on R, we assume that u is doubling, and we…
The doubly minimized Petz Renyi mutual information (PRMI) of order $\alpha$ is defined as the minimization of the Petz divergence of order $\alpha$ of a fixed bipartite quantum state $\rho_{AB}$ relative to any product state…
In this article, we give a definition for measured quantum groupoids. We want to get objects with duality extending both quantum groups and groupoids. We base ourselves on J. Kustermans and S. Vaes' works about locally compact quantum…
Let $P:=\frac 1 3 P\circ S_1^{-1}+\frac 13 P\circ S_2^{-1}+\frac 13\nu$, where $S_1(x)=\frac 15 x$, $S_2(x)=\frac 1 5 x+\frac 45$ for all $x\in \mathbb R$, and $\nu$ be a Borel probability measure on $\mathbb R$ with compact support. Such a…
We provide an algorithm to approximate a finitely supported discrete measure $\mu$ by a measure $\nu_{N}$ corresponding to a set of $N$ points so that the total variation between $\mu$ and $\nu_N$ has an upper bound. As a consequence if…
The Born rule for probabilities of measurement results is deduced from the set of five assumptions. The assumptions state that: (a) the state vector fully determines the probabilities of all measurement results; (b) between measurements,…
Let $E$ be a Bedford-McMullen carpet determined by a set of affine mappings $(f_{ij})_{(i,j)\in G}$ and $\mu$ a self-affine measure on $E$ associated with a probability vector $(p_{ij})_{(i,j)\in G}$. We prove that, for every…
Quantum-enhanced measurements exploit quantum mechanical effects to provide ultra-precise estimates of physical variables for use in advanced technologies, such as frequency calibration of atomic clocks, gravitational waves detection, and…
Quantum measurements based on mutually unbiased bases are commonly used in quantum information processing, as they are generally viewed as being maximally incompatible and complementary. Here we quantify precisely the degree of…
We show that correlations inconsistent with any locally causal description can be a generic feature of measurements on entangled quantum states. Specifically, spatially-separated parties who perform local measurements on a…
The problem of binary hypothesis testing between two probability measures is considered. New sharp bounds are derived for the best achievable error probability of such tests based on independent and identically distributed observations.…
We study the convergence rate of the optimal quantization for a probability measure sequence $(\mu_{n})_{n\in\mathbb{N}^{*}}$ on $\mathbb{R}^{d}$ converging in the Wasserstein distance in two aspects: the first one is the convergence rate…
The quantization scheme in probability theory deals with finding a best approximation of a given probability distribution by a probability distribution that is supported on finitely many points. For a given $k\geq 2$, let $\{S_j : 1\leq…
We elucidate the asymptotics of the L^s-quantization error induced by a sequence of L^r-optimal n-quantizers of a probability distribution P on R^d when s>r. In particular we show that under natural assumptions, the optimal rate is…
The minimum probability of error (MPE) measurement discriminates between a set of candidate quantum states with the minimum average error probability allowed by quantum mechanics. Conditions for a measurement to be MPE were derived by Yuen,…