Related papers: A Converse Bound via the Nussbaum-Szko{\l}a Mappin…

We prove the converse part of the theorem for quantum Hoeffding bound on the asymptotics of quantum hypothesis testing, essentially based on an argument developed by Nussbaum and Szkola in proving the converse part of the quantum Chernoff…

We consider symmetric hypothesis testing in quantum statistics, where the hypotheses are density operators on a finite-dimensional complex Hilbert space, representing states of a finite quantum system. We prove a lower bound on the…

Hypothesis exclusion is an information-theoretic task in which an experimenter aims at ruling out a false hypothesis from a finite set of known candidates, and an error occurs if and only if the hypothesis being ruled out is the ground…

We consider the asymmetric formulation of quantum hypothesis testing, where two quantum hypotheses have different associated costs. In this problem, the aim is to minimize the probability of false negatives and the optimal performance is…

The laws of quantum mechanics place fundamental limits on the accuracy of measurements and therefore on the estimation of unknown parameters of a quantum system. In this work, we prove lower bounds on the size of confidence regions reported…

The polynomial method by Beals, Buhrman, Cleve, Mosca, and de Wolf (FOCS 1998, J. ACM 2001), the adversary method by Ambainis (STOC 2000, J. Comput. Syst. Sci. 2002), and the compressed oracle method by Zhandry (CRYPTO 2019) have been shown…

This thesis addresses the interplay between asymptotic hypothesis testing and entropy inequalities in quantum information theory. In the first part of the thesis we focus on hypothesis testing. We consider two main settings; one can either…

We extend quantum Stein's lemma in asymmetric quantum hypothesis testing to composite null and alternative hypotheses. As our main result, we show that the asymptotic error exponent for testing convex combinations of quantum states…

Quantum information theory sets the ultimate limits for any information-processing task. In rangefinding and LIDAR, the presence or absence of a target can be tested by detecting different states at the receiver. In this Letter, we use…

We uncover the quantum fluctuation-response inequality, which, in the most general setting, establishes a bound for the mean difference of an observable at two different quantum states, in terms of the quantum relative entropy. When the…

Alternative exact expressions are derived for the minimum error probability of a hypothesis test discriminating among $M$ quantum states. The first expression corresponds to the error probability of a binary hypothesis test with certain…

Two types of errors can occur when discriminating pairs of quantum states. Asymmetric state discrimination involves minimizing the probability of one type of error, subject to a constraint on the other. We give explicit expressions bounding…

The ultimate limits of quantum state discrimination are often thought to be captured by asymptotic bounds that restrict the achievable error probabilities, notably the quantum Chernoff and Hoeffding bounds. Here we study hypothesis testing…

In the simple quantum hypothesis testing problem, upper bound with asymmetric setting is shown by using a quite useful inequality by Audenaert et al, quant-ph/0610027, which was originally invented for symmetric setting. Using this upper…

Detecting the presence of multiple incoherent sources is a fundamental and challenging task for quantum imaging, especially within sub-Rayleigh region. In this paper, the discrimination of one-versus-two point-like incoherent sources in…

We consider the multiple hypothesis testing problem for symmetric quantum state discrimination between r given states \sigma_1,...,\sigma_r. By splitting up the overall test into multiple binary tests in various ways we obtain a number of…

The number of times that we can access a system to extract information via quantum metrology is always finite, and possibly small, and realistic amounts of prior knowledge tend to be moderate. Thus theoretical consistency demands a…

In statistical inference problems, we wish to obtain lower bounds on the minimax risk, that is to bound the performance of any possible estimator. A standard technique to obtain risk lower bounds involves the use of Fano's inequality. In an…

We study a variant of quantum hypothesis testing wherein an additional 'inconclusive' measurement outcome is added, allowing one to abstain from attempting to discriminate the hypotheses. The error probabilities are then conditioned on a…

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…