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The application of oscillatory flow around an obstacle drives a steady ``streaming'' due to inertial rectification, which has been used in a host of microfluidic applications. While theory has focused largely on two-dimensional (2D) flows,…

Fluid Dynamics · Physics 2023-05-10 Xirui Zhang , Bhargav Rallabandi

We show that the minimum von-Neumann entropy output of a quantum channel is locally additive. Hasting's counterexample for the additivity conjecture, makes this result quite surprising. In particular, it indicates that the non-additivity of…

Quantum Physics · Physics 2012-10-03 Gilad Gour , Shmuel Friedland

In this paper, we consider the minimal entropy of qubit states transmitted through two uses of a noisy quantum channel, which is modeled by the action of a completely positive trace-preserving (or stochastic) map. We provide strong support…

Quantum Physics · Physics 2007-05-23 C. King , M. B. Ruskai

We study the classical problem of characterizing the channel capacity and its achieving distribution in a generic fashion. We derive a simple relation between three parameters: the input-output function, the input cost function and the…

Information Theory · Computer Science 2017-11-17 Jihad Fahs , Ibrahim Abou-Faycal

The additivity of the minimal output entropy and that of the $\chi$-capacity are known to be equivalent for finite-dimensional irreducibly covariant channels. In this paper we formulate a list of conditions allowing to establish similar…

Quantum Physics · Physics 2018-12-12 A. S. Holevo

Quantum channels can represent dynamic resources, which are indispensable elements in many physical scenarios. To describe certain facets of nonclassicality of the channels, it is necessary to quantify their properties. In the framework of…

Quantum Physics · Physics 2022-11-23 Huaqi Zhou , Ting Gao , Fengli Yan

The goal of this note is to show that the analysis of the minimum output p-Renyi entropy of a typical quantum channel essentially amounts to applying Milman's version of Dvoretzky's Theorem about almost Euclidean sections of…

Quantum Physics · Physics 2010-02-07 Guillaume Aubrun , Stanislaw Szarek , Elisabeth Werner

In this article, we investigate the additivity phenomenon in the dynamic capacity of a quantum channel for trading classical communication, quantum communication and entanglement. Understanding such additivity property is important if we…

Quantum Physics · Physics 2017-08-17 Elton Yechao Zhu , Quntao Zhuang , Min-Hsiu Hsieh , Peter W. Shor

Recently Hastings proved the existence of random unitary channels which violate the additivity conjecture. In this paper we use Hastings' method to derive new bounds for the entanglement of random subspaces of bipartite systems. As an…

Quantum Physics · Physics 2014-11-27 Motohisa Fukuda , Christopher King

Zero-error coding encompasses a variety of source and channel problems where the probability of error must be exactly zero. This condition is stricter than that of the vanishing error regime, where the error probability goes to zero as the…

Information Theory · Computer Science 2025-12-02 Nicolas Charpenay , Maël Le Treust , Aline Roumy

Using the concept of discrete noiseless channels, it was shown by Shannon in A Mathematical Theory of Communication that the ultimate performance of an encoder for a constrained system is limited by the combinatorial capacity of the system…

Information Theory · Computer Science 2008-09-09 Georg Böcherer , Valdemar Cardoso da Rocha , Cecilio Pimentel

We prove bounds for the number of solutions to $$a_1 + \dots + a_k = a_1' + \dots + a_k'$$ over $N$-element sets of reals, which are sufficiently convex or near-convex. A near-convex set will be the image of a set with small additive…

Number Theory · Mathematics 2021-04-26 Peter J. Bradshaw , Brandon Hanson , Misha Rudnev

For all p > 1, we demonstrate the existence of quantum channels with non-multiplicative maximal output p-norms. Equivalently, for all p >1, the minimum output Renyi entropy of order p of a quantum channel is not additive. The violations…

Quantum Physics · Physics 2012-07-06 Patrick Hayden , Andreas Winter

Recently, the projective robustness of quantum states has been introduced in [arXiv:2109.04481(2021)]. It shows that the projective robustness is a useful resource monotone and can comprehensively characterize capabilities and limitations…

Quantum Physics · Physics 2022-06-15 Mingfei Ye , Yu Luo , Zhihui Li , Yongming Li

Inspired by Montanaro's work, we introduce the concept of additivity rates of a quantum channel $L$, which give the first order (linear) term of the minimum output $p$-R\'enyi entropies of $L^{\otimes r}$ as functions of $r$. We lower bound…

Mathematical Physics · Physics 2015-10-15 Motohisa Fukuda , Ion Nechita

The coding theorem for the entanglement-assisted communication via infinite-dimensional quantum channel with linear constraint is extended to a natural degree of generality. Relations between the entanglement-assisted classical capacity and…

Mathematical Physics · Physics 2013-05-29 A. S. Holevo , M. E. Shirokov

In this paper we fill the gap in previous works by proving the formula for entanglement-assisted capacity of quantum channel with additive constraint (such as bosonic Gaussian channel). The main tools are the coding theorem for…

Quantum Physics · Physics 2009-11-07 A. S. Holevo

A condition for reversibility (sufficiency) of a channel with respect to a given countable family of states with bounded rank is obtained. This condition shows that a quantum channel preserving the Holevo quantity of at least one (discrete…

Quantum Physics · Physics 2013-11-12 M. E. Shirokov

This paper presents a counterexample to the optimality conjecture in convex quantum channel optimization proposed by Coutts et al. The conjecture posits that for nuclear norm minimization problems in quantum channel optimization, the dual…

Quantum Physics · Physics 2026-02-03 Jianting Yang

According to Blackwell's Theorem it is equivalent to compare channels by either a garbling order or optimal decision making. This equivalence does not hold anymore if also allowing pre-garbling, i. e. for the so-called Shannon-order (see…

Optimization and Control · Mathematics 2019-06-18 Sebastian Lämmel , Vladimir Shikhman