Related papers: Generalized quantum asymptotic equipartition
Based on trajectory dependent path probability formalism in state space, we derive generalized entropy production fluctuation relations for a quantum system in the presence of measurement and feedback. We have obtained these results for…
The eigenstate thermalization hypothesis (ETH) provides a powerful framework for understanding thermalization in isolated quantum many-body systems, yet a complete and conceptually transparent derivation has remained elusive. In this work,…
When two independent analog signals, X and Y are added together giving Z=X+Y, the entropy of Z, H(Z), is not a simple function of the entropies H(X) and H(Y), but rather depends on the details of X and Y's distributions. Nevertheless, the…
We study asymptotic state transformations in continuous variable quantum resource theories. In particular, we prove that monotones displaying lower semicontinuity and strong superadditivity can be used to bound asymptotic transformation…
Regularized kernel methods such as, e.g., support vector machines and least-squares support vector regression constitute an important class of standard learning algorithms in machine learning. Theoretical investigations concerning…
We consider nonparametric testing in a non-asymptotic framework. Our statistical guarantees are exact in the sense that Type I and II errors are controlled for any finite sample size. Meanwhile, one proposed test is shown to achieve minimax…
We show that quantification of the performance of quantum-enhanced measurement schemes based on the concept of quantum Fisher information yields asymptotically equivalent results as the rigorous Bayesian approach, provided generic…
It is a fundamental prediction of quantum theory that states of physical systems are described by complex vectors or density operators on a Hilbert space. However, many experiments admit effective descriptions in terms of other state…
In standard quantum theory, the ideas of information-entropy and of pure states are closely linked. States are represented by density matrices $\rho$ on a Hilbert space and the information-entropy $-tr(\rho\log\rho)$ is minimised on pure…
Various measures have been suggested recently for quantifying the coherence of a quantum state with respect to a given basis. We first use two of these, the l_1-norm and relative entropy measures, to investigate tradeoffs between the…
Randomization tests are based on a re-randomization of existing data to gain data-dependent critical values that lead to exact hypothesis tests under special circumstances. However, it is not always possible to re-randomize data in…
Entanglement is a quantum resource, in some ways analogous to randomness in classical computation. Inspired by recent work of Gheorghiu and Hoban, we define the notion of "pseudoentanglement'', a property exhibited by ensembles of…
We consider a generalized model of repeated quantum interactions, where a system $\mathcal{H}$ is interacting in a random way with a sequence of independent quantum systems $\mathcal{K}_n, n \geq 1$. Two types of randomness are studied in…
The ultimate limits of quantum state discrimination are often thought to be captured by asymptotic bounds that restrict the achievable error probabilities, notably the quantum Chernoff and Hoeffding bounds. Here we study hypothesis testing…
The theory of local asymptotic normality for quantum statistical experiments is developed in the spirit of the classical result from mathematical statistics due to Le Cam. Roughly speaking, local asymptotic normality means that the family…
In this article, we explore properties of pseudo entropy [1] in quantum field theories and spin systems from several approaches. Pseudo entropy is a generalization of entanglement entropy such that it depends on both an initial and final…
We propose a general measure of non-classical correlations for bipartite systems based on generalized entropic functions and majorization properties. Defined as the minimum information loss due to a local measurement, in the case of pure…
Randomized experiments have become important tools in empirical research. In a completely randomized treatment-control experiment, the simple difference in means of the outcome is unbiased for the average treatment effect, and covariate…
This paper studies the asymptotic power of tests of sphericity against perturbations in a single unknown direction as both the dimensionality of the data and the number of observations go to infinity. We establish the convergence, under the…
The entropic uncertainty principle in the form proven by Maassen and Uffink yields a fundamental inequality that is prominently used in many places all over the field of quantum information theory. In this work, we provide a family of…