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The entanglement entropy of a pure quantum state of a bipartite system $A \cup B$ is defined as the von Neumann entropy of the reduced density matrix obtained by tracing over one of the two parts. Critical ground states of local…

Strongly Correlated Electrons · Physics 2008-11-26 Eduardo Fradkin , Joel E. Moore

A common approach to evaluate entropy in quantum systems is to solve a master-Bloch equation to determine density matrix and substitute it in entropy definition. However, this method has been recently understood to lack many energy…

High Energy Physics - Theory · Physics 2016-05-17 Mohammad H Ansari

We present a diffeomorphism-invariant formulation of differential entropy for Riemannian spaces, providing a fine-grained, coordinate-independent notion of quantum information for continuous variables in physical space. To this end, we…

Quantum Physics · Physics 2025-05-16 Pablo G. Camara

Bell's inequalities, in the form given by Cerf and Adami, are derived from the combination of the second law of thermodynamics and the Markov postulate. Violations of these inequalities are discussed in terms of the mixing characteristics…

Quantum Physics · Physics 2007-05-23 Ian T. Durham

Uncertainty relations provide constraints on how well the outcomes of incompatible measurements can be predicted, and, as well as being fundamental to our understanding of quantum theory, they have practical applications such as for…

Quantum Physics · Physics 2013-05-30 Patrick J. Coles , Roger Colbeck , Li Yu , Michael Zwolak

By extending the concept of energy-constrained diamond norms, we obtain continuity bounds on the dynamics of both closed and open quantum systems in infinite-dimensions, which are stronger than previously known bounds. We extensively…

Quantum Physics · Physics 2020-01-08 Simon Becker , Nilanjana Datta

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…

Quantum Physics · Physics 2016-09-06 Andreas Winter

Using Fourier analysis, we derive Wirtinger-type inequalities of arbitrary high order. As applications, we prove various sharp geometric inequalities for closed curves on the Euclidean plane. In particular, we obtain both sharp lower and…

Differential Geometry · Mathematics 2020-08-18 Kwok-Kun Kwong , Hojoo Lee

Strong subadditivity of von Neumann entropy, proved in 1973 by Lieb and Ruskai, is a cornerstone of quantum coding theory. All other known inequalities for entropies of quantum systems may be derived from it. Here we prove a new inequality…

Quantum Physics · Physics 2007-05-23 Noah Linden , Andreas Winter

We present observable upper bounds of squared concurrence, which are the dual inequalities of the observable lower bounds introduced in [F. Mintert and A. Buchleitner, Phys. Rev. Lett. 98, 140505 (2007)] and [L. Aolita, A. Buchleitner and…

Quantum Physics · Physics 2009-11-13 Cheng-Jie Zhang , Yan-Xiao Gong , Yong-Sheng Zhang , Guang-Can Guo

Most of the existing classification methods are aimed at minimization of empirical risk (through some simple point-based error measured with loss function) with added regularization. We propose to approach this problem in a more information…

Machine Learning · Computer Science 2015-01-22 Wojciech Marian Czarnecki , Jacek Tabor

Large-scale quantum networks have been employed to overcome practical constraints of transmissions and storage for single entangled systems. Our goal in this article is to explore the strong entanglement distribution of quantum networks. We…

Quantum Physics · Physics 2022-04-18 Xue Yang , Yan-Han Yang , Ming-Xing Luo

We study the notion of approximate entropy within the framework of network theory. Approximate entropy is an uncertainty measure originally proposed in the context of dynamical systems and time series. We firstly define a purely structural…

Disordered Systems and Neural Networks · Physics 2013-05-30 James West , Lucas Lacasa , Simone Severini , Andrew Teschendorff

We prove sharp $\ell^q L^p$ decoupling inequalities for $p,q \in [2,\infty)$ and arbitrary tuples of quadratic forms. Connections to prior results on decoupling inequalities for quadratic forms are also explained. We also include some…

Classical Analysis and ODEs · Mathematics 2023-03-22 Shaoming Guo , Changkeun Oh , Ruixiang Zhang , Pavel Zorin-Kranich

It is known that the variance and entropy of quantum observables decompose into intrinsically quantum and classical contributions. Here a general method of constructing quantum-classical decompositions of resources such as uncertainty is…

Quantum Physics · Physics 2023-07-07 Michael J. W. Hall

Under a precise genuine nonlinearity assumption we establish the decay of entropy solutions of a multidimensional scalar conservation law with merely continuous flux.

Analysis of PDEs · Mathematics 2019-04-03 Evgeny Yu. Panov

We introduce a complex purity density and its associated current for pure states of continuous variable systems. The scheme is constructed by analogy with the notions of probability density and probability current. Taking advantage of the…

Quantum Physics · Physics 2020-06-16 Pedro Sancho

We study regularization for the deep linear network (DLN) using the entropy formula introduced in arXiv:2509.09088. The equilibria and gradient flow of the free energy on the Riemannian manifold of end-to-end maps of the DLN are…

Neural and Evolutionary Computing · Computer Science 2025-12-09 Alan Chen , Tejas Kotwal , Govind Menon

We extend our studies of holographic entropy inequalities to gapped phases of matter. For any number of regions, we determine the linear entropy inequalities satisfied by systems in which the entanglement entropy satisfies an exact area…

High Energy Physics - Theory · Physics 2015-10-02 Ning Bao , ChunJun Cao , Michael Walter , Zitao Wang

We argue from the point of view of statistical inference that the quantum relative entropy is a good measure for distinguishing between two quantum states (or two classes of quantum states) described by density matrices. We extend this…

Quantum Physics · Physics 2009-10-30 V. Vedral , M. B. Plenio , K. Jacobs , P. L. Knight