Related papers: Optimized quantum f-divergences
This work advances the theoretical understanding of quantum learning by establishing a new family of upper bounds on the expected generalization error of quantum learning algorithms, leveraging the framework introduced by Caro et al. (2024)…
It is well known that for pure states the relative entropy of entanglement is equal to the reduced entropy, and the closest separable state is explicitly known as well. The same holds for Renyi relative entropy per recent results. We ask…
We investigate quantum R\'enyi entropic quantities, specifically those derived from 'sandwiched' divergence. This divergence is one of several proposed R\'enyi generalisations of the quantum relative entropy. We may define R\'enyi…
The R{\'e}nyi entropy is one of the important information measures that generalizes Shannon's entropy. The quantum R{\'e}nyi entropy has a fundamental role in quantum information theory, therefore, bounding this quantity is of vital…
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…
Quantum information quantities play a substantial role in characterizing operational quantities in various quantum information-theoretic problems. We consider numerical computation of four quantum information quantities: Petz-Augustin…
R\'enyi and Augustin information are generalizations of mutual information defined via the R\'enyi divergence, playing a significant role in evaluating the performance of information processing tasks by virtue of its connection to the error…
The maximum-likelihood principle unifies inference of quantum states and processes from experimental noisy data. Particularly, a generic quantum process may be estimated simultaneously with unknown quantum probe states provided that…
The relative entropy between quantum states quantifies their distinguishability. The estimation of certain relative entropies has been investigated in the literature, e.g., the von Neumann relative entropy and sandwiched R\'enyi relative…
The development of quantum computation has resulted in many quantum algorithms for a wide array of tasks. Recently, there is a growing interest in using quantum computing techniques to estimate or compute quantum information-theoretic…
In this paper we deal with two quantum relative entropy preserver problems on the cones of positive (either positive definite or positive semidefinite) operators. The first one is related to a quantum R\'enyi relative entropy like quantity…
An essential quantity in quantum information theory is the von Neumann entropy which depends entirely on the quantum density operator. Once known, the density operator reveals the statistics of observables in a quantum process, and the…
Information-theoretic measures such as relative entropy and correlation are extremely useful when modeling or analyzing the interaction of probabilistic systems. We survey the quantum generalization of 5 such measures and point out some of…
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…
Special approximation technique for analysis of different characteristics of states of multipartite infinite-dimensional quantum systems is proposed and applied to study of the relative entropy of entanglement and its regularisation. We…
Lieb and Ruskai's strong subadditivity theorem, which shows that the conditional mutual information must be nonnegative, is fundamental in quantum theory. It has numerous applications, such as in quantum error correction. When the mutual…
Quantifying entanglement is a work in progress which is important for the active field of quantum information and computation. A measure of bipartite pure state entanglement is proposed here, named entanglement coherence, which is…
The quantum relative entropy between two states satisfies a monotonicity property meaning that applying the same quantum channel to both states can never increase their relative entropy. It is known that this inequality is only tight when…
Quantum information decoupling is a fundamental quantum information processing task, which also serves as a crucial tool in a diversity of topics in quantum physics. In this paper, we characterize the reliability function of catalytic…
We define a new divergence of von Neumann algebras using a variational expression that is similar in nature to Kosaki's formula for the relative entropy. Our divergence satisfies the usual desirable properties, upper bounds the sandwiched…