Sumiyoshi Abe
Nonadditive (nonextensive) generalization of the quantum Kullback-Leibler divergence, termed the quantum q-divergence, is shown not to increase by projective measurements in an elementary manner.
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The Kullback-Leibler divergence offers an information-theoretic basis for measuring the difference between two given distributions. Its quantum analog, however, fails to play a corresponding role for comparing two density matrices, if the reference states are pure states. Here, it is shown that nonadditive (nonextensive) generalization of quantum information theory is free from such a difficulty and the associated quantity, termed the quantum q-divergence, can in fact be a good information-theoretic measure of the degree of purification. The correspondence relation between the ordinary diverge…
Monotonicity of optimized quantum $f$-divergence
本研究针对Wilde提出的优化量子$f$-散度单调性能否推广至非量子信道映射的问题，证明其单调性可推广到满足施瓦茨不等式的正保迹映射，解答了该公开问题。
Monotonic multi-state quantum $f$-divergences
本文利用模理论和算子平均构造了一类满足数据处理不等式的多态量子 $f$-散度，统一了多种已知散度，并猜想其具有量子态区分中的操作意义。
Quantum f-divergences are a quantum generalization of the classical notion of f-divergences, and are a special case of Petz' quasi-entropies. Many well known distinguishability measures of quantum states are given by, or derived from, f-divergences; special examples include the quantum relative entropy, the Renyi relative entropies, and the Chernoff and Hoeffding measures. Here we show that the quantum f-divergences are monotonic under the dual of Schwarz maps whenever the defining function is operator convex. This extends and unifies all previously known monotonicity results. We also analyze …
The concept of classical $f$-divergences gives a unified framework to construct and study measures of dissimilarity of probability distributions; special cases include the relative entropy and the Rényi divergences. Various quantum versions of this concept, and more narrowly, the concept of Rényi divergences, have been introduced in the literature with applications in quantum information theory; most notably Petz' quasi-entropies (standard $f$-divergences), Matsumoto's maximal $f$-divergences, measured $f$-divergences, and sandwiched and $α$-$z$-Rényi divergences. In this paper we give a syste…
A unified framework of unitarily residual measures for quantifying dissipation
本文提出酉残余测度统一框架，通过分离非酉分量并在酉变换商集上诱导酉不变散度度量，为开放量子系统耗散量化提供新工具。
The minimal memory required to model a given stochastic process - known as the statistical complexity - is a widely adopted quantifier of structure in complexity science. Here, we ask if quantum mechanics can fundamentally change the qualitative behaviour of this measure. We study this question in the context of the classical Ising spin chain. In this system, the statistical complexity is known to grow monotonically with temperature. We evaluate the spin chain's quantum mechanical statistical complexity by explicitly constructing its provably simplest quantum model, and demonstrate that this m…
We characterize the functions for which the corresponding Bregman divergence is jointly convex on matrices. As an application of this characterization, we derive a sharp inequality for the quantum Tsallis entropy of a tripartite state, which can be considered as a generalization of the strong subadditivity of the von Neumann entropy. (In general, the strong subadditivity of the Tsallis entropy fails for quantum states, but it holds for classical states.) Furthermore, we show that the joint convexity of the Bregman divergence does not imply the monotonicity under stochastic maps, but every mono…
Some properties and applications of the new quantum $f$-divergences
本文研究新型量子 $f$-散度的替代表达式，据此证明其单调性、凸性及与 Rényi 散度相关的不等式，并给出量子 Chernoff 界可达性的新证明。
The information spectrum approach gives general formulae for optimal rates of codes in many areas of information theory. In this paper the quantum spectral divergence rates are defined and properties of the rates are derived. The entropic rates, conditional entropic rates, and spectral mutual information rates are then defined in terms of the spectral divergence rates. Properties including subadditivity, chain rules, Araki-Lieb inequalities, and monotonicity are then explored.
Integral formula for quantum relative entropy implies data processing inequality
本文建立了量子相对熵及von Neumann熵高阶导数的积分表示，简化证明了Holevo界和量子相对熵单调性等数据处理不等式，并展示了其在量子散度及信息论概率模型中的应用。
Induced Quantum Divergence: A New Lens on Communication and Source Coding
本文提出由母量子相对熵导出的诱导量子散度，用以替代基于位置解码中的假设检验散度，从而简化量子通信与状态重分配分析并获得更紧界。
Cumulant-based quantum relative Rényi functional
提出一种基于累积量生成函数的新型量子相对Rényi泛函作为候选量子Rényi散度，在支持条件下建立了基本性质，并引入正则化版本研究非对易性刻画。
Geodesic Quantum $f$-Divergences
本文引入测地量子f-散度，证明其满足数据处理不等式，确定其等号情况及可逆测地量子马尔可夫链的坍缩，还分析了参数单调性等性质，为量子信息领域提供了新的散度工具。
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