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Related papers: Quantum hypothesis testing with group symmetry

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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…

Quantum Physics · Physics 2015-09-04 Gaetana Spedalieri , Samuel L. Braunstein

There are fundamental limits to the accuracy with which one can determine the state of a quantum system. I give an overview of the main approaches to quantum state discrimination. Several strategies exist. In quantum hypothesis testing, a…

Quantum Physics · Physics 2009-11-06 Anthony Chefles

We derive a necessary and sufficient condition for a sequence of quantum measurements to achieve the optimal performance in quantum hypothesis testing. Using an information-spectrum method, we discuss what quantum measurement we should…

Quantum Physics · Physics 2009-11-07 Masahito Hayashi

We report a proof of the quantum Sanov Theorem by elementary application of basic facts about representations of the symmetric group, together with a complete characterization of the optimal error exponent in a situation where the null…

Quantum Physics · Physics 2015-06-17 J. Nötzel

One of the fundamental tenets of quantum mechanics is that non-orthogonal states cannot be distinguished perfectly. When distinguishing multiple copies of a mixed quantum state, a collective measurement, which generates entanglement between…

Quantum Physics · Physics 2025-04-02 Lorcan Conlon , Jin Ming Koh , Biveen Shajilal , Jasminder Sidhu , Ping Koy Lam , Syed M. Assad

We investigate the nonparametric, composite hypothesis testing problem for arbitrary unknown distributions in the asymptotic regime where both the sample size and the number of hypotheses grow exponentially large. Such asymptotic analysis…

Information Theory · Computer Science 2019-01-30 Qunwei Li , Tiexing Wang , Donald J. Bucci , Yingbin Liang , Biao Chen , Pramod K. Varshney

We derive a bound on the precision of state estimation for finite dimensional quantum systems and prove its attainability in the generic case where the spectrum is non-degenerate. Our results hold under an assumption called local asymptotic…

Quantum Physics · Physics 2019-05-09 Yuxiang Yang , Giulio Chiribella , Masahito Hayashi

Given a mixture of states, finding a way to optimally discriminate its elements is a prominent problem in quantum communication theory. In this paper, we will address mixtures of density operators that are unitarily equivalent via elements…

Mathematical Physics · Physics 2024-02-09 Alberto Acevedo , Janek Wehr

By invoking quantum estimation theory we formulate bounds of errors in quantum measurement for arbitrary quantum states and observables in a finite-dimensional Hilbert space. We prove that the measurement errors of two observables satisfy…

Quantum Physics · Physics 2013-05-29 Yu Watanabe , Takahiro Sagawa , Masahito Ueda

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

The definition of a quantum state corresponding to a wave packet far from a global soliton is considered. We define an asymptotic quantum state corresponding to a localized wave packet of elementary quanta far from a kink. We demand that…

High Energy Physics - Theory · Physics 2023-04-05 Jarah Evslin

In the simple quantum hypothesis testing problem, upper bounds on the error probabilities are shown based on a key operator inequality between a density operator and its pinching. Concerning the error exponents, the upper bounds lead to a…

Quantum Physics · Physics 2007-05-23 Tomohiro Ogawa , Masahito Hayashi

We study the local indistinguishability problem of quantum states. By introducing an easily calculated quantity, non-commutativity, we present an criterion which is both necessary and sufficient for the local indistinguishability of a…

Quantum Physics · Physics 2014-09-17 Teng Ma , Ming-Jing Zhao , Yao-Kun Wang , Shao-Ming Fei

Motivated by the recent discovery of a quantum Chernoff theorem for asymptotic state discrimination, we investigate the distinguishability of two bipartite mixed states under the constraint of local operations and classical communication…

Quantum Physics · Physics 2011-03-16 William Matthews , Andreas Winter

One of the key tasks in physics is to perform measurements in order to determine the state of a system. Often, measurements are aimed at determining the values of physical parameters, but one can also ask simpler questions, such as "is the…

Quantum Physics · Physics 2021-07-01 Jan de Boer , Victor Godet , Jani Kastikainen , Esko Keski-Vakkuri

Quantum hypothesis testing (QHT) provides an effective method to discriminate between two quantum states using a two-outcome positive operator-valued measure (POVM). Two types of decision errors in a QHT can occur. In this paper we focus on…

Quantum Physics · Physics 2023-07-13 Yi Shen , Carlo Maria Scandolo , Lin Chen

We show finite-size bounds on the deviation of the optimal type II error from its asymptotic value in the quantum hypothesis testing problem of Stein's lemma with composite null-hypothesis. The proof is based on some simple properties of a…

Quantum Physics · Physics 2014-07-07 Milán Mosonyi

This expository article gives an overview of the theory of hypothesis testing of quantum states in finite dimensional Hilbert spaces. Optimal measurement strategy for testing binary quantum hypotheses, which result in minimum error…

Quantum Physics · Physics 2018-03-14 J. Prabhu Tej , Syed Raunaq Ahmed , A. R. Usha Devi , A. K. Rajagopal

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

In the problem of asymptotic binary i.i.d. state discrimination, the optimal asymptotics of the type I and the type II error probabilities is in general an exponential decrease to zero as a function of the number of samples; the set of…

Quantum Physics · Physics 2023-01-18 Gergely Bunth , Gábor Maróti , Milán Mosonyi , Zoltán Zimborás