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Related papers: Quantum f-divergences and error correction

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We introduce measurement-based quantum diffusion models that bridge classical and quantum diffusion theory through randomized weak measurements. The measurement-based approach naturally generates stochastic quantum trajectories while…

Quantum Physics · Physics 2026-05-12 Xinyu Liu , Jingze Zhuang , Wanda Hou , Yi-Zhuang You

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

The distinguishability between two quantum states can be defined in terms of their trace distance. The operational meaning of this definition involves a maximization over measurement projectors. Here we introduce an alternative definition…

Quantum Physics · Physics 2024-09-04 Adrian A. Budini , Ruynet L. de Matos Filho , Marcelo F. Santos

In this work we investigate how to quantify the coherence of quantum measurements. First, we establish a resource theoretical framework to address the coherence of measurement and show that any statistical distance can be adopted to define…

Quantum Physics · Physics 2020-08-11 Kyunghyun Baek , Adel Sohbi , Jaehak Lee , Jaewan Kim , Hyunchul Nha

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

The Einstein-Podolsky-Rosen (EPR) paradox plays a fundamental role in our understanding of quantum mechanics, and is associated with the possibility of predicting the results of non-commuting measurements with a precision that seems to…

Quantum Physics · Physics 2022-07-13 Benjamin Yadin , Matteo Fadel , Manuel Gessner

We characterize the asymptotic performance of a class of positive operator valued measurements (POVMs) where the only task is to make measurements on independent and identically distributed quantum states on finite-dimensional systems. The…

Quantum Physics · Physics 2016-11-24 Janis Nötzel

We develop a rigorous framework for quantifying quantum coherence in finite-dimensional systems by applying the Schur-Horn majorization theorem to relate eigenvalue distributions and diagonal entries of density matrices. Building on this…

Quantum Physics · Physics 2025-06-06 Tariq Aziz , Meng-Long Song , Liu Ye , Dong Wang

Let $Q$ be a nonempty closed and convex subset of a real Hilbert space $% \mathcal{H}$. $T:Q\rightarrow Q$ is a nonexpansive mapping which has a least one fixed point. $f:Q\rightarrow \mathcal{H}$ is a Lipschitzian function, and $%…

Dynamical Systems · Mathematics 2021-12-23 Ramzi May , Zahrah Bin Ali

Integral representations of quantum relative entropy, and of the directional second and higher order derivatives of von Neumann entropy, are established, and used to give simple proofs of fundamental, known data processing inequalities: the…

Quantum Physics · Physics 2023-09-13 Péter E. Frenkel

The quantum \chi^2-divergence has recently been introduced and applied to quantum channels (quantum Markov processes). In contrast to the classical setting the quantum \chi^2-divergence is not unique but depends on the choice of quantum…

Mathematical Physics · Physics 2012-10-02 Frank Hansen

We systematically study the fundamental competition between quantum error correction (QEC) and continuous symmetries, two key notions in quantum information and physics, in a quantitative manner. Three meaningful measures of approximate…

Quantum Physics · Physics 2023-12-14 Zi-Wen Liu , Sisi Zhou

To find the essential nature of quantum theory has been an important problem for not only theoretical interest but also applications to quantum technologies. In those studies on quantum foundations, the notion of uncertainty plays a primary…

Quantum Physics · Physics 2022-03-01 Ryo Takakura

Some of the important inequalities associated with quantum entropy are immediate algebraic consequences of the Hansen-Pedersen-Jensen inequality. A general argument is given using matrix perspectives of operator convex functions. A matrix…

Mathematical Physics · Physics 2009-11-13 Edward G. Effros

We provide in a unified way quantitative forms of strong convergence results for numerous iterative procedures which satisfy a general type of Fejer monotonicity where the convergence uses the compactness of the underlying set. These…

Logic · Mathematics 2015-08-25 Ulrick Kohlenbach , Laurentiu Leustean , Adriana Nicolae

In the context of measurement-based quantum computation a way of maintaining the coherence of a graph state is to measure its stabilizer operators. Aside from performing quantum error correction, it is possible to exploit the information…

Quantum Physics · Physics 2016-04-06 Davide Orsucci , Markus Tiersch , Hans J. Briegel

We discuss the argument proposed in Ref.~\cite{Frauchiger-Renner}, and show that it does not particularly illustrate any inconsistency in quantum mechanics, but rather the well known difficulty often described as the \textquotedblleft…

Quantum Physics · Physics 2018-07-10 F. Laloë

In the framework of quantum information geometry we investigate the relationship between monotone metric tensors uniquely defined on the space of quantum tomograms, once the tomographic scheme chosen, and monotone quantum metrics on the…

Mathematical Physics · Physics 2017-12-01 Marco Laudato , Giuseppe Marmo , Fabio M. Mele , Franco Ventriglia , Patrizia Vitale

Recently, there has been focus on determining the conditions under which the data processing inequality for quantum relative entropy is satisfied with approximate equality. The solution of the exact equality case is due to Petz, who showed…

Quantum Physics · Physics 2018-02-22 Ludovico Lami , Siddhartha Das , Mark M. Wilde

In prior work, we have shown how the basic concepts and terms of quantum mechanics relate to factorizations and marginals of complex-valued quantum mass functions, which are generalizations of joint probability mass functions. In this…

Quantum Physics · Physics 2019-10-08 Hans-Andrea Loeliger , Pascal O. Vontobel