Related papers: An invitation to the sample complexity of quantum …
This paper investigates symmetric composite binary quantum hypothesis testing (QHT), where the goal is to determine which of two uncertainty sets contains an unknown quantum state. While asymptotic error exponents for this problem are…
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 hypothesis testing (QHT) concerns the statistical inference of unknown quantum states. In the general setting of composite hypotheses, the goal of QHT is to determine whether an unknown quantum state belongs to one or another of two…
Quantum channel discrimination has been studied from an information-theoretic perspective, wherein one is interested in the optimal decay rate of error probabilities as a function of the number of unknown channel accesses. In this paper, we…
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…
Hoeffding's formulation and solution to the universal hypothesis testing (UHT) problem had a profound impact on many subsequent works dealing with asymmetric hypotheses. In this work, we introduce a quantum universal hypothesis testing…
We study hypothesis testing under communication constraints, where each sample is quantized before being revealed to a statistician. Without communication constraints, it is well known that the sample complexity of simple binary hypothesis…
The task of binary quantum hypothesis testing is to determine the state of a quantum system via measurements on it, given the side information that it is in one of two possible states, say $\rho$ and $\sigma$. This task is generally studied…
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 state discrimination is an important problem in many information processing tasks. In this work we are concerned with finding its best possible sample complexity when the states are preprocessed by a quantum channel that is required…
We investigate the sample complexity of Hamiltonian simulation: how many copies of an unknown quantum state are required to simulate a Hamiltonian encoded by the density matrix of that state? We show that the procedure proposed by Lloyd,…
We study the composite sequential quantum hypothesis testing (SQHT) problem, where the objective is to distinguish a null quantum state from a set of alternative quantum states. We propose a mixture-sequential quantum probability ratio test…
This thesis aims to establish notions of symmetry for quantum states and channels as well as describe algorithms to test for these properties on quantum computers. Ideally, the work will serve as a self-contained overview of the subject. We…
This paper investigates Distributed Hypothesis testing (DHT), in which a source $\mathbf{X}$ is encoded given that side information $\mathbf{Y}$ is available at the decoder only. Based on the received coded data, the receiver aims to decide…
Symmetry plays a crucial role in quantum physics, dictating the behavior and dynamics of physical systems. In this paper, we develop a hypothesis-testing framework for quantum dynamics symmetry using a limited number of queries to the…
A central problem in Binary Hypothesis Testing (BHT) is to determine the optimal tradeoff between the Type I error (referred to as false alarm) and Type II (referred to as miss) error. In this context, the exponential rate of convergence of…
The sample complexity of simple binary hypothesis testing is the smallest number of i.i.d.\ samples required to distinguish between two distributions $p$ and $q$ in either: (i) the prior-free setting, with type-I error at most $\alpha$ and…
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 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…
This paper investigates practical coding schemes for Distributed Hypothesis Testing (DHT). While the literature has extensively analyzed the information-theoretic performance of DHT and established bounds on Type-II error exponents through…