Related papers: On Composite Quantum Hypothesis Testing
Proving threshold theorems for fault-tolerant quantum computation is a burdensome endeavor with many moving parts that come together in relatively formulaic but lengthy ways. It is difficult and rare to combine elements from multiple papers…
We present a quantum extension of a version of Sanov's theorem focussing on a hypothesis testing aspect of the theorem: There exists a sequence of typical subspaces for a given set $\Psi$ of stationary quantum product states asymptotically…
We treat quantum counterparts of testing problems whose optimal tests are given by chi-square, t and F tests. These quantum counterparts are formulated as quantum hypothesis testing problems concerning quantum Gaussian states families, and…
Quantum state tomography on a d-dimensional system demands resources that grow rapidly with d. They may be reduced by using model selection to tailor the number of parameters in the model (i.e., the size of the density matrix). Most model…
Entanglement-based attacks, which are subtle and powerful, are usually believed to render quantum bit commitment insecure. We point out that the no-go argument leading to this view implicitly assumes the evidence-of-commitment to be a…
Quantum measurements can produce randomness arising from the uncertainty principle. When measuring a state with von Neumann measurements, the intrinsic randomness can be quantified by the quantum coherence of the state on the measurement…
We extend the mathematical theory of quantum hypothesis testing to the general $W^*$-algebraic setting and explore its relation with recent developments in non-equilibrium quantum statistical mechanics. In particular, we relate the large…
This thesis consolidates, improves and extends the smooth entropy framework for non-asymptotic information theory and cryptography. We investigate the conditional min- and max-entropy for quantum states, generalizations of classical R\'enyi…
Quantum key distribution (QKD) achieves information-theoretic security, without relying on computational assumptions, by distributing quantum states. To establish secret bits, two honest parties exploit key distillation protocols over…
We consider the problem of sequentially testing a simple null hypothesis versus a composite alternative hypothesis that consists of a finite set of densities. We study sequential tests that are based on thresholding of mixture-based…
This paper places conformal testing in a general framework of statistical hypothesis testing. A standard approach to testing a composite null hypothesis $H$ is to test each of its elements and to reject $H$ when each of its elements is…
We consider two variants of a quantum-statistical generalization of the Cramer-Rao inequality that establishes an invariant lower bound on the mean square error of a generalized quantum measurement. The proposed complex variant of this…
We provide a new general theorem for multivariate normal approximation on convex sets. The theorem is formulated in terms of a multivariate extension of Stein couplings. We apply the results to a homogeneity test in dense random graphs and…
Estimation of quantum relative entropy and its R\'{e}nyi generalizations is a fundamental statistical task in quantum information theory, physics, and beyond. While several estimators of these divergences have been proposed in the…
The minimax robust hypothesis testing problem for the case where the nominal probability distributions are subject to both modeling errors and outliers is studied in twofold. First, a robust hypothesis testing scheme based on a relative…
Integral representations of quantum relative entropy, and of the directional second and higher order derivatives of von Neumann entropy, are established, and used to give simple proofs of fundamental, known data processing inequalities: the…
We present an analytical formula for the asymptotic relative entropy of entanglement for Werner states of arbitrary dimension. We then demonstrate its validity using methods from convex optimization. To our knowledge, this is the first case…
To find the essential nature of quantum theory has been an important problem for not only theoretical interest but also applications to quantum technologies. In those studies on quantum foundations, the notion of uncertainty plays a primary…
We prove the converse part of the theorem for quantum Hoeffding bound on the asymptotics of quantum hypothesis testing, essentially based on an argument developed by Nussbaum and Szkola in proving the converse part of the quantum Chernoff…
Many trace inequalities can be expressed either as concavity/convexity theorems or as monotonicity theorems. A classic example is the joint convexity of the quantum relative entropy which is equivalent to the Data Processing Inequality. The…