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We consider two different optimized measurement strategies for the discrimination of nonorthogonal quantum states. The first is conclusive discrimination with a minimum probability of inferring an erroneous result, and the second is…

Quantum Physics · Physics 2009-11-10 Ulrike Herzog , Janos A. Bergou

We provide new non-asymptotic false discovery proportion (FDP) confidence envelopes in several multiple testing settings relevant for modern high dimensional-data methods. We revisit the multiple testing scenarios considered in the recent…

Statistics Theory · Mathematics 2024-09-18 Iqraa Meah , Gilles Blanchard , Etienne Roquain

Pairs of states, or "boxes" are the basic objects in the resource theory of asymmetric distinguishability (Wang and Wilde, 2019), where free operations are arbitrary quantum channels that are applied to both states. From this point of view,…

Quantum Physics · Physics 2021-07-28 Gergely Bunth , Péter Vrana

Quantum state discrimination enables the accurate identification of quantum states, which are generally nonorthogonal. Among various strategies, minimum-error discrimination and unambiguous state discrimination exhibit…

Quantum Physics · Physics 2026-02-24 Min Namkung , Hyang-Tag Lim

We consider asymptotic hypothesis testing (or state discrimination with asymmetric treatment of errors) between an arbitrary fixed bipartite pure state $\ket{\Psi}$ and the completely mixed state under one-way LOCC (local operations and…

Quantum Physics · Physics 2024-09-10 Masahito Hayashi , Masaki Owari

We present novel bounds for estimating discrete probability distributions under the $\ell_\infty$ norm. These are nearly optimal in various precise senses, including a kind of instance-optimality. Our data-dependent convergence guarantees…

Statistics Theory · Mathematics 2024-02-14 Aryeh Kontorovich , Amichai Painsky

The trade-off between the two types of errors in binary state discrimination may be quantified in the asymptotics by various error exponents. In the case of simple i.i.d. hypotheses, each of these exponents is equal to a divergence…

Quantum Physics · Physics 2023-01-18 Milán Mosonyi , Zsombor Szilágyi , Mihály Weiner

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 Physics · Physics 2021-07-26 Mario Berta , Fernando G. S. L. Brandao , Christoph Hirche

The problem of multiple hypothesis testing with observation control is considered in both fixed sample size and sequential settings. In the fixed sample size setting, for binary hypothesis testing, the optimal exponent for the maximal error…

Information Theory · Computer Science 2013-09-05 Sirin Nitinawarat , George Atia , Venugopal V. Veeravalli

An active hypothesis testing problem is formulated. In this problem, the agent can perform a fixed number of experiments and then decide on one of the hypotheses. The agent is also allowed to declare its experiments inconclusive if needed.…

Information Theory · Computer Science 2019-01-23 Dhruva Kartik , Ashutosh Nayyar , Urbashi Mitra

We use the smooth entropy approach to treat the problems of binary quantum hypothesis testing and the transmission of classical information through a quantum channel. We provide lower and upper bounds on the optimal type II error of quantum…

Quantum Physics · Physics 2013-12-11 Nilanjana Datta , Milan Mosonyi , Min-Hsiu Hsieh , Fernando G. S. L. Brandao

We revisit the fundamental question of simple-versus-simple hypothesis testing with an eye towards computational complexity, as the statistically optimal likelihood ratio test is often computationally intractable in high-dimensional…

Statistics Theory · Mathematics 2025-05-05 Ankur Moitra , Alexander S. Wein

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…

Information Theory · Computer Science 2022-03-30 Jiachun Pan , Yonglong Li , Vincent Y. F. Tan

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…

Quantum Physics · Physics 2014-12-23 Michael Walter , Joseph M. Renes

It is well-known that observing nonlocal correlations allows us to draw conclusions about the quantum systems under consideration. In some cases this yields a characterisation which is essentially complete, a phenomenon known as…

Quantum Physics · Physics 2020-04-02 Tim Coopmans , Jędrzej Kaniewski , Christian Schaffner

Transductive conformal prediction addresses the simultaneous prediction for multiple data points. Given a desired confidence level, the objective is to construct a prediction set that includes the true outcomes with the prescribed…

Machine Learning · Computer Science 2025-09-08 Arash Behboodi , Alvaro H. C. Correia , Fabio Valerio Massoli , Christos Louizos

Reliability of sequential hypothesis testing can be greatly improved when the decision maker is given the freedom to adaptively take an action that determines the distribution of the current collected sample. Such advantage of sampling…

Information Theory · Computer Science 2025-07-11 Chia-Yu Hsu , I-Hsiang Wang

In the asymptotic theory of quantum hypothesis testing, the minimal error probability of the first kind jumps sharply from zero to one when the error exponent of the second kind passes by the point of the relative entropy of the two states…

Quantum Physics · Physics 2014-02-28 Ke Li

Quantum discord has been utilised in order to find quantum advantage in an extension of the Clauser, Horne, Shimony, and Holt (CHSH) game. By writing the game explicitly as a Bayesian game, the resulting game is modified such the payoff's…

Quantum Physics · Physics 2023-06-09 Adam Lowe

Previous studies in quantum information have recognized that specific types of noise can encode information in certain applications. However, the role of noise in Quantum Hypothesis Testing (QHT), traditionally assumed to undermine…

Quantum Physics · Physics 2024-08-06 Qing Li , Lingna Wang , Min Jiang , Ze Wu , Haidong Yuan , Xinhua Peng