Related papers: Upper bounds on the error probabilities and asympt…
We prove non-asymptotic error bounds for Sequential MCMC methods in the case of multimodal target distributions. Our bounds depend in an explicit way on upper bounds on relative densities, on constants associated with local mixing…
The Chernoff bound is a well-known tool for obtaining a high probability bound on the expectation of a Bernoulli random variable in terms of its sample average. This bound is commonly used in statistical learning theory to upper bound the…
We investigate the performance of discrimination strategy in the comparison task of known quantum states. In the discrimination strategy, one infers whether or not two quantum systems are in the same state on the basis of the outcomes of…
We theoretically investigate schemes to discriminate between two nonorthogonal quantum states given multiple copies. We consider a number of state discrimination schemes as applied to nonorthogonal, mixed states of a qubit. In particular,…
We provide an exact non-asymptotic lower bound on the minimax expected excess risk (EER) in the agnostic probably-ap\-proximately-correct (PAC) machine learning classification model and identify minimax learning algorithms as certain…
In this note we consider the finite-dimensional parameter estimation problem associated to inverse problems. In such scenarios, one seeks to maximize the marginal likelihood associated to a Bayesian model. This latter model is connected to…
We present an efficient parallel derandomization method for randomized algorithms that rely on concentrations such as the Chernoff bound. This settles a classic problem in parallel derandomization, which dates back to the 1980s. Consider…
We study the first- and second-order asymptotics of covert communication over binary-input DMC for three different covertness metrics and under maximum probability of error constraint. When covertness is measured in terms of the relative…
Quantum illumination employs entangled states to detect a weakly reflective target in a thermal bath. The performance of a given entangled state is evaluated from the minimum error probability in the asymptotic limit, which is compared…
The existing upper and lower bounds between entropy and error probability are mostly derived from the inequality of the entropy relations, which could introduce approximations into the analysis. We derive analytical bounds based on the…
An identity between two versions of the Chernoff bound on the probability a certain large deviations event, is established. This identity has an interpretation in statistical physics, namely, an isothermal equilibrium of a composite system…
We investigate generalized measurements, based on positive-operator-valued measures, and von Neumann measurements for the unambiguous discrimination of two mixed quantum states that occur with given prior probabilities. In particular, we…
Recent advances in noiseless non-adaptive group testing have led to a precise asymptotic characterization of the number of tests required for high-probability recovery in the sublinear regime $k = n^{\theta}$ (with $\theta \in (0,1)$), with…
We consider the sequential composite binary hypothesis testing problem in which one of the hypotheses is governed by a single distribution while the other is governed by a family of distributions whose parameters belong to a known set…
We consider the problem of hypothesis testing for discrete distributions. In the standard model, where we have sample access to an underlying distribution $p$, extensive research has established optimal bounds for uniformity testing,…
We investigate the problem of jointly testing multiple hypotheses and estimating a random parameter of the underlying distribution in a sequential setup. The aim is to jointly infer the true hypothesis and the true parameter while using on…
Finding the closest separable state to a given target state is a notoriously difficult task, even more difficult than deciding whether a state is entangled or separable. To tackle this task, we parametrize separable states with a neural…
We introduce sequential analysis in quantum information processing, by focusing on the fundamental task of quantum hypothesis testing. In particular our goal is to discriminate between two arbitrary quantum states with a prescribed error…
We study an optimized measurement that discriminates two mixed quantum states with maximum confidence for each conclusive result, thereby keeping the overall probability of inconclusive results as small as possible. When the rank of the…
We consider the task of quantum state certification: given a description of a hypothesis state $\sigma$ and multiple copies of an unknown state $\rho$, a tester aims to determine whether the two states are equal or $\epsilon$-far in trace…