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The data processing inequality states that the quantum relative entropy between two states $\rho$ and $\sigma$ can never increase by applying the same quantum channel $\mathcal{N}$ to both states. This inequality can be strengthened with a…

Quantum Physics · Physics 2018-09-14 Marius Junge , Renato Renner , David Sutter , Mark M. Wilde , Andreas Winter

Holevo's just-as-good fidelity is a similarity measure for quantum states that has found several applications. One of its critical properties is that it obeys a data processing inequality: the measure does not decrease under the action of a…

Quantum Physics · Physics 2018-12-24 Mark M. Wilde

Distance measures between quantum states like the trace distance and the fidelity can naturally be defined by optimizing a classical distance measure over all measurement statistics that can be obtained from the respective quantum states.…

Quantum Physics · Physics 2017-11-09 Mario Berta , Omar Fawzi , Marco Tomamichel

Two typical fixed-length random number generation problems in information theory are considered for general sources. One is the source resolvability problem and the other is the intrinsic randomness problem. In each of these problems, the…

Information Theory · Computer Science 2024-05-14 Ryo Nomura , Hideki Yagi

Based on the resource theory for quantifying the coherence of quantum channels, we introduce a new coherence quantifier for quantum channels via maximum relative entropy. We prove that the maximum relative entropy for coherence of quantum…

This paper develops systematic approaches to obtain $f$-divergence inequalities, dealing with pairs of probability measures defined on arbitrary alphabets. Functional domination is one such approach, where special emphasis is placed on…

Information Theory · Computer Science 2016-12-06 Igal Sason , Sergio Verdú

Discriminating between noisy quantum processes is a central primitive for quantum communication, metrology, and computing. While discrimination limits for finite-dimensional channels are well understood, the continuous-variable setting,…

Quantum Physics · Physics 2026-03-23 Zixin Huang , Ludovico Lami , Vishal Singh , Mark M. Wilde

We provide the sandwiched R\'enyi divergence of order $\alpha\in(\frac{1}{2},1)$, as well as its induced quantum information quantities, with an operational interpretation in the characterization of the exact strong converse exponents of…

Quantum Physics · Physics 2024-05-29 Ke Li , Yongsheng Yao

Smooth Csisz\'ar $f$-divergences can be expressed as integrals over so-called hockey stick divergences. This motivates a natural quantum generalization in terms of quantum Hockey stick divergences, which we explore here. Using this recipe,…

Quantum Physics · Physics 2024-08-27 Christoph Hirche , Marco Tomamichel

The $\alpha$-sandwiched R\'enyi divergence satisfies the data processing inequality, i.e. monotonicity under quantum operations, for $\alpha\geq 1/2$. In this article, we derive a necessary and sufficient algebraic condition for equality in…

Quantum Physics · Physics 2017-12-15 Felix Leditzky , Cambyse Rouzé , Nilanjana Datta

The quantum relative entropy is a fundamental quantity in quantum information science, characterizing the distinguishability between two quantum states. However, this quantity is not additive in general for correlated quantum states,…

Quantum Physics · Physics 2025-06-05 Kun Fang , Hamza Fawzi , Omar Fawzi

Quantum relative entropy, a quantum generalization of the renowned Kullback-Leibler divergence, serves as a fundamental measure of the distinguishability between quantum states and plays a pivotal role in quantum information science.…

Quantum Physics · Physics 2025-10-02 Yuchen Lu , Kun Fang

Quantum error correction (QEC) is an essential concept for any quantum information processing device. Typically, QEC is designed with minimal assumptions about the noise process; this generic assumption exacts a high cost in efficiency and…

Quantum Physics · Physics 2007-06-26 Andrew S. Fletcher

We study the Hoeffding regime of composite quantum hypothesis testing, in which each hypothesis is specified by a sequence of sets of quantum states. We establish quantum Hoeffding bounds under a set of structural assumptions, orthogonal to…

Quantum Physics · Physics 2026-05-05 Masahito Hayashi , Kun Fang

This paper introduces a method for calculating the quantum relative entropy of channels, an essential quantity in quantum channel discrimination and resource theories of quantum channels. By building on recent developments in the…

Quantum Physics · Physics 2026-04-16 Gereon Koßmann , Mark M. Wilde

Quantum channel estimation and discrimination are fundamentally related information processing tasks of interest in quantum information science. In this paper, we analyze these tasks by employing the right logarithmic derivative Fisher…

Quantum Physics · Physics 2021-03-02 Vishal Katariya , Mark M. Wilde

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)…

Quantum Physics · Physics 2026-04-20 Naqueeb Ahmad Warsi , Ayanava Dasgupta , Masahito Hayashi

Quantum Internet relies on quantum entanglement as a fundamental resource for secure and efficient quantum communication, reshaping data transmission. In this context, entanglement distillation emerges as a crucial process that plays a…

Quantum Physics · Physics 2024-07-30 Chengkai Zhu , Chenghong Zhu , Xin Wang

We analyze how an action of a qubit channel (map) can be estimated from the measured data that are incomplete or even inconsistent. That is, we consider situations when measurement statistics is insufficient to determine consistent…

Quantum Physics · Physics 2009-11-10 Mario Ziman , Martin Plesch , Vladimir Buzek

This work provides data-processing and majorization inequalities for $f$-divergences, and it considers some of their applications to coding problems. This work also provides tight bounds on the R\'{e}nyi entropy of a function of a discrete…

Information Theory · Computer Science 2021-04-01 Igal Sason