Related papers: A limit of the quantum Renyi divergence
Uncertainty relations provide constraints on how well the outcomes of incompatible measurements can be predicted, and, as well as being fundamental to our understanding of quantum theory, they have practical applications such as for…
In the problem of binary quantum channel discrimination with product inputs, the supremum of all type II error exponents for which the optimal type I errors go to zero is equal to the Umegaki channel relative entropy, while the infimum of…
In this paper a new operational definition of Renyi entropy and Renyi divergence is presented. Other operational definitions are mentioned.
We prove that the quantum relative entropy is a rate function in large deviation principle. Next, we define information criteria for quantum states and estimate the accuracy of the use of them. Most of the results in this paper are…
We consider the maximum entropy problems associated with R\'enyi $Q$-entropy, subject to two kinds of constraints on expected values. The constraints considered are a constraint on the standard expectation, and a constraint on the…
Entanglement R\'enyi-$\alpha$ entropy is an entanglement measure. It generalizes the entanglement of formation, and they coincide when $\alpha$ tends to 1. We derive analytical lower and upper bounds for the entanglement R\'enyi-$\alpha$…
In this paper, we establish a general relation which directly links the dissipated work done on a system driven arbitrarily far from equilibrium, a fundamental quantity in thermodynamics, and the R\'{e}nyi divergences, a fundamental concept…
The aim of the present paper is to give axiomatic characterization of quantum relative entropy utilizing resource conversion scenario. We consider two sets of axioms: non-asymptotic and asymptotic. In the former setting, we prove that the…
The optimized quantum $f$-divergences form a family of distinguishability measures that includes the quantum relative entropy and the sandwiched R\'enyi relative quasi-entropy as special cases. In this paper, we establish physically…
The max-relative entropy and the conditional min-entropy it induces have become central to one-shot information theory. Both may be expressed in terms of a conic program over the positive semidefinite cone. Recently, it was shown that the…
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…
In local quantum circuits with charge conservation, we initialize the system in random product states and study the dynamics of the Renyi entanglement entropy $R_\alpha$. We rigorously prove that $R_\alpha$ with Renyi index $\alpha>1$ at…
We consider the problem of approximating the empirical Shannon entropy of a high-frequency data stream under the relaxed strict-turnstile model, when space limitations make exact computation infeasible. An equivalent measure of entropy is…
Radical-ion-pair reactions were recently shown to manifest a host of non-trivial quantum effects accounted for by quantum measurement theory. An alternative approach purporting to describe the fundamental quantum dynamics of spin-selective…
B. Schumacher and M. Westmoreland have established a quantum analog of a well-known classical information theory result on a role of relative entropy as a measure of non-optimality in (classical) data compression. In this paper, we provide…
A framework for a quantum mechanical information theory is introduced that is based entirely on density operators, and gives rise to a unified description of classical correlation and quantum entanglement. Unlike in classical (Shannon)…
In recent years, the Renyi entropy has repeatedly been discussed for characterization of quantum critical states and entanglement. Here, time evolution of the Renyi entropy is studied. A compact general formula is presented for the lower…
Renyi reflected entropies of order $n \geq 2$ are correlation measures that have been introduced in the field of holography. In this work, we put the spotlight on the min-reflected entropy, i.e., the Renyi reflected entropy in the limit $n…
Formalising the confrontation of opinions (models) to observations (data) is the task of Inferential Statistics. Information Theory provides us with a basic functional, the relative entropy (or Kullback-Leibler divergence), an asymmetrical…
The $\alpha$-$z$ R\'enyi relative entropies are a two-parameter family of R\'enyi relative entropies that are quantum generalizations of the classical $\alpha$-R\'enyi relative entropies. In \cite{zhang20CFL} we decided the full range of…