相关论文: A tight uniform continuity bound for the Arimoto-R…

The classical asymptotic equipartition property is the statement that, in the limit of a large number of identical repetitions of a random experiment, the output sequence is virtually certain to come from the typical set, each member of…

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 study R\'enyi entropy of locally excited states with considering the thermal and boundary effects respectively in two dimensional conformal field theories (CFTs). Firstly we consider locally excited states obtained by acting primary…

Basic properties of the unified entropies are examined. The consideration is mainly restricted to the finite-dimensional quantum case. Bounds in terms of ensembles of quantum states are given. Both the continuity in Fannes' sense and…

In a closed system, the total number of particles is fixed. We ask how much does this conservation law restrict the amount of entanglement that can be created. We derive a tight upper bound on the bipartite entanglement entropy in closed…

The ground state entanglement entropy is studied in a many-body bipartite quantum system with either a single or multiple conserved quantities. It is shown that the entanglement entropy exhibits a universal power-law behaviour at large $R$…

A fundamental result in modern quantum chaos theory is the Maldacena-Shenker-Stanford upper bound on the growth of out-of-time-order correlators, whose infinite-temperature limit is related to the operator-space entanglement entropy of the…

We describe a modification of the Alicki-Fannes-Winter method which allows to prove uniform continuity on the set of quantum states with bounded energy of any locally almost affine function having limited growth with increasing energy. Some…

We show that for any $\alpha>0$ the R\'enyi entropy of order $\alpha$ is minimized, among all symmetric log-concave random variables with fixed variance, either for a uniform distribution or for a two sided exponential distribution. The…

This paper introduces "swiveled Renyi entropies" as an alternative to the Renyi entropic quantities put forward in [Berta et al., Phys. Rev. A 91, 022333 (2015)]. What distinguishes the swiveled Renyi entropies from the prior proposal of…

Relative entropy is a measure of distinguishability for quantum states, and plays a central role in quantum information theory. The family of Renyi entropies generalizes to Renyi relative entropies that include as special cases most entropy…

The max-relative entropy together with its smoothed version is a basic tool in quantum information theory. In this paper, we derive the exact exponent for the asymptotic decay of the small modification of the quantum state in smoothing the…

This thesis addresses the interplay between asymptotic hypothesis testing and entropy inequalities in quantum information theory. In the first part of the thesis we focus on hypothesis testing. We consider two main settings; one can either…

Configurational entropy, or complexity, plays a critical role in characterizing disordered systems such as glasses, yet its measurement often requires significant computational resources. Recently, R\'enyi entropy, a one-parameter…

Unraveling the secrets of how much nonstabilizerness a quantum dynamic can generate is crucial for harnessing the power of magic states, the essential resources for achieving quantum advantage and realizing fault-tolerant quantum…

We give a simple proof of the uncertainty principle with quantum side information, as in [Berta et al. Nature Physics 6, 659 (2010)], invoking the monotonicity of the relative entropy. Our proof shows that the entropic uncertainty principle…

Following a recent proof of Shannon's entropy power inequality (EPI), a comprehensive framework for deriving various EPIs for the R\'enyi entropy is presented that uses transport arguments from normal densities and a change of variable by…

Uncertainty relations based on quantum coherence is an important problem in quantum information science. We discuss uncertainty relations for averaged unified ($\alpha$,$\beta$)-relative entropy of coherence under mutually unbiased…

The fully quantum reverse Shannon theorem establishes the optimal rate of noiseless classical communication required for simulating the action of many instances of a noisy quantum channel on an arbitrary input state, while also allowing for…

Distributions of abundances or frequencies play an important role in many fields of science, from biology to sociology, as does the R\'enyi entropy, which measures the diversity of a statistical ensemble. We derive a mathematical relation…