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In the classical many normal means with different variances, we consider the situation when the observer is allowed to allocate the available measurement budget over the coordinates of the parameter of interest. The benchmark is the minimax…

Statistics Theory · Mathematics 2019-04-01 Eduard Belitser

We study the problem of estimating, in the sense of optimal transport metrics, a measure which is assumed supported on a manifold embedded in a Hilbert space. By establishing a precise connection between optimal transport metrics, optimal…

Machine Learning · Computer Science 2012-09-06 Guillermo D. Canas , Lorenzo Rosasco

Quantum state discrimination, alongside its other applications, has recently found use as a tool for witnessing generalised contextuality. In this article, we derive noncontextuality inequalities for both conclusive and inconclusive…

Quantum Physics · Physics 2025-11-07 Kieran Flatt , Joonwoo Bae

For a binary system specified by the density operators r0 and r1 and by the prior probabilities q0 and q1, Helstrom's theory permits the evaluation of the optimal measurement operators and of the corresponding maximum correct detection…

Information Theory · Computer Science 2010-10-27 Gianfranco Cariolaro , Alberto Vigato

We interpret likelihood-based test functions from a geometric perspective where the Kullback-Leibler (KL) divergence is adopted to quantify the distance from a distribution to another. Such a test function can be seen as a sub-Gaussian…

Information Theory · Computer Science 2021-01-05 Yan Wang

We improve some upper bounds for minimal dispersion on the cube and torus. /Our new ingredient is an improvement of a probabilistic lemma used to obtain upper bounds for dispersion in several previous works. Our new lemma combines a random…

Metric Geometry · Mathematics 2024-06-06 Andrii Arman , Alexander E. Litvak

During recent years the interest of optimization and machine learning communities in high-probability convergence of stochastic optimization methods has been growing. One of the main reasons for this is that high-probability complexity…

Recently, Arjevani et al. [1] established a lower bound of iteration complexity for the first-order optimization under an $L$-smooth condition and a bounded noise variance assumption. However, a thorough review of existing literature on…

Machine Learning · Computer Science 2023-10-30 Bohan Wang , Jingwen Fu , Huishuai Zhang , Nanning Zheng , Wei Chen

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…

Quantum Physics · Physics 2009-11-13 Ulrike Herzog

This work discusses how to derive upper bounds for the expected generalisation error of supervised learning algorithms by means of the chaining technique. By developing a general theoretical framework, we establish a duality between…

Machine Learning · Statistics 2022-07-01 Eugenio Clerico , Amitis Shidani , George Deligiannidis , Arnaud Doucet

We discuss a novel implementation of the minimum error state discrimination measurement, originally introduced by Helstrom. In this implementation, instead of performing the optimal projective measurement directly on the system, it is first…

Quantum Physics · Physics 2020-03-11 Rui Han , Gerd Leuchs , János A. Bergou

One of the most fascinating aspects of quantum mechanics is the principle impossibility of deterministic errorless discrimination of nonorthogonal signals, such as coherent states. On the one hand, it prevents perfect cloning of quantum…

Quantum Physics · Physics 2017-01-10 Denis Sych , Gerd Leuchs

For a coherent, binary system made up of binary elements, the exact failure probability requires knowledge of statistical dependence of all orders among the minimal cut sets. Since dependence among the cut sets beyond the second order is…

Probability · Mathematics 2023-03-20 Sourangshu Ghosh , Baidurya Bhattacharya

The impossibility of deterministic and error-free discrimination among nonorthogonal quantum states lies at the core of quantum theory and constitutes a primitive for secure quantum communication. Demanding determinism leads to errors,…

Quantum Physics · Physics 2021-12-21 M. A. Solís-Prosser , O. Jiménez , A. Delgado , L. Neves

In modern scientific research, small-scale studies with limited participants are increasingly common. However, interpreting individual outcomes can be challenging, making it standard practice to combine data across studies using random…

Statistics Theory · Mathematics 2025-11-04 Lucas Kania , Larry Wasserman , Sivaraman Balakrishnan

The discrimination of quantum states is a central problem in quantum information science and technology. Meanwhile, partial post-selection has emerged as a valuable tool for quantum state engineering. In this work, we bring these two areas…

Quantum Physics · Physics 2026-04-14 Qipeng Qian , Christos N. Gagatsos

Given a mixture between two populations of coins, "positive" coins that each have -- unknown and potentially different -- bias $\geq\frac{1}{2}+\Delta$ and "negative" coins with bias $\leq\frac{1}{2}-\Delta$, we consider the task of…

Machine Learning · Computer Science 2021-02-08 Jasper C. H. Lee , Paul Valiant

Quantum state tomography is a fundamental problem in quantum computing. Given $n$ copies of an unknown $N$-qubit state $\rho \in \mathbb{C}^{d \times d},d=2^N$, the goal is to learn the state up to an accuracy $\epsilon$ in trace distance,…

Quantum Physics · Physics 2025-02-26 Jayadev Acharya , Abhilash Dharmavarapu , Yuhan Liu , Nengkun Yu

A finite horizon variant of the quickest change detection problem is studied, in which the goal is to minimize a delay threshold (latency), under constraints on the probability of false alarm and the probability that the latency is…

Data Structures and Algorithms · Computer Science 2024-09-20 Yu-Han Huang , Venugopal V. Veeravalli

Quantum state exclusion is an operational task with application to ontological interpretations of quantum states. In such a task, one is given a system whose state is randomly selected from a finite set, and the goal is to identify a state…

Quantum Physics · Physics 2026-03-25 Kaiyuan Ji , Hemant K. Mishra , Milán Mosonyi , Mark M. Wilde