Related papers: Second-order asymptotics for quantum hypothesis te…
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…
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…
We study quantum soft covering and privacy amplification against quantum side information. The former task aims to approximate a quantum state by sampling from a prior distribution and querying a quantum channel. The latter task aims to…
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…
In this MSc thesis I consider the asymptotic behaviour of the symmetric error in composite hypothesis testing. In the classical case, when the null and alternative hypothesis are finite sets of states, the best achievable symmetric error…
Motivated by real-world machine learning applications, we analyze approximations to the non-asymptotic fundamental limits of statistical classification. In the binary version of this problem, given two training sequences generated according…
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…
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…
This paper deals with order identification for nested models in the i.i.d. framework. We study the asymptotic efficiency of two generalized likelihood ratio tests of the order. They are based on two estimators which are proved to be…
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 consider the problem of detecting the true quantum state among $r$ possible ones, based of measurements performed on $n$ copies of a finite-dimensional quantum system. A special case is the problem of discriminating between $r$…
The asymptotic equipartition property (AEP) states that in the limit of a large number of independent and identically distributed (i.i.d.) random experiments, the output sequence is virtually certain to come from the typical set, each…
We give a rigorous treatment on the foundation of the first order asymptotic theory of quantum estimation, with tractable and reasonable regularity conditions. Different from past works, we do not use Fisher information nor MLE, and an…
This monograph presents a unified treatment of single- and multi-user problems in Shannon's information theory where we depart from the requirement that the error probability decays asymptotically in the blocklength. Instead, the error…
We study the error exponents in quantum hypothesis testing between two sets of quantum states, extending the analysis beyond the independent and identically distributed case to encompass composite correlated hypotheses. In particular, we…
We derived an asymptotic bound the accuracy of the estimation when we use the quantum correlation in the measuring apparatus. It is also proved that this bound can be achieved in any model in the quantum two-level system. Moreover, we show…
The generalized quantum Stein's lemma provides an explicit expression for the optimal error exponent when distinguishing many independent and identically distributed (iid) copies of a given bipartite state from the set of separable…
Quantum hypothesis testing is one of the most basic tasks in quantum information theory and has fundamental links with quantum communication and estimation theory. In this paper, we establish a formula that characterizes the decay rate of…
We study sequential multiple testing with independent data streams, where the goal is to identify an unknown subset of signals while controlling commonly used error metrics, including generalized familywise rates and false discovery and…
Due to the difficulties of implementing joint measurements, quantum illumination schemes that are based on signal-idler entanglement are difficult to implement in practice. For this reason, one may consider quantum-inspired designs of…