Advanced Alicki-Fannes-Winter method for energy-constrained quantum systems and its use

通过几乎凸性证明量子熵量的连续性

Continuity of quantum entropic quantities via almost convexity

本文提出ALAFF方法，基于条件熵连续性证明，推导多种量子熵量的连续性界，得到新结果并证明相关熵的几乎凹性，可应用于量子信息领域。

Tight continuity bounds for the quantum conditional mutual information, for the Holevo quantity and for capacities of quantum channels

We start with Fannes' type and Winter's type tight continuity bounds for the quantum conditional mutual information and their specifications for states of special types. Then we analyse continuity of the Holevo quantity with respect to nonequivalent metrics on the set of discrete ensembles of quantum states. We show that the Holevo quantity is continuous on the set of all ensembles of m states with respect to all the metrics if either m or the dimension of underlying Hilbert space is finite and obtain Fannes' type tight continuity bounds for the Holevo quantity in this case. In general case co…

Tight uniform continuity bounds for quantum entropies: conditional entropy, relative entropy distance and energy constraints

We present a bouquet of continuity bounds for quantum entropies, falling broadly into two classes: First, a tight analysis of the Alicki-Fannes continuity bounds for the conditional von Neumann entropy, reaching almost the best possible form that depends only on the system dimension and the trace distance of the states. Almost the same proof can be used to derive similar continuity bounds for the relative entropy distance from a convex set of states or positive operators. As applications we give new proofs, with tighter bounds, of the asymptotic continuity of the relative entropy of entangleme…

Classical information capacity of a class of quantum channels

We consider the additivity of the minimal output entropy and the classical information capacity of a class of quantum channels. For this class of channels the norm of the output is maximized for the output being a normalized projection. We prove the additivity of the minimal output Renyi entropies with entropic parameters contained in [0, 2], generalizing an argument by Alicki and Fannes, and present a number of examples in detail. In order to relate these results to the classical information capacity, we introduce a weak form of covariance of a channel. We then identify several instances of w…

关于sandwiched Rényi和Tsallis条件熵的连续性不等式及其在信道熵连续性中的应用

Continuity inequalities for sandwiched Rényi and Tsallis conditional entropies with application to the channel entropy continuity

本文研究了sandwiched Rényi和Tsallis条件熵的连续性不等式，证明了在信道熵定义中通过相对熵的连续性。

The quantum dynamic capacity formula of a quantum channel

The dynamic capacity theorem characterizes the reliable communication rates of a quantum channel when combined with the noiseless resources of classical communication, quantum communication, and entanglement. In prior work, we proved the converse part of this theorem by making contact with many previous results in the quantum Shannon theory literature. In this work, we prove the theorem with an "ab initio" approach, using only the most basic tools in the quantum information theorist's toolkit: the Alicki-Fannes' inequality, the chain rule for quantum mutual information, elementary properties o…