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As shown by M\'edard, the capacity of fading channels with imperfect channel-state information (CSI) can be lower-bounded by assuming a Gaussian channel input $X$ with power $P$ and by upper-bounding the conditional entropy $h(X|Y,\hat{H})$…

Information Theory · Computer Science 2016-11-15 Adriano Pastore , Tobias Koch , Javier Rodríguez Fonollosa

We present an equilibrium statistical-mechanical theory of selectivity in biological ion channels. In doing so, we introduce a grand canonical ensemble for ions in a channel's selectivity filter coupled to internal and external bath…

Biological Physics · Physics 2016-05-11 D. G. Luchinsky , W. A. T. Gibby , I. Kaufman , D. A. Timucin , P. V. E. McClintock

Additivity of the Holevo capacity is proved for product channels, under the condition that one of the channels is in a certain class of unital qubit channels, with the other completely arbitrary. This qubit class includes the depolarizing…

Quantum Physics · Physics 2015-06-26 C. King

We investigate the generic aspects of quantum coherence guided by the concentration of measure phenomenon. We find the average relative entropy of coherence of pure quantum states sampled randomly from the uniform Haar measure and show that…

Quantum Physics · Physics 2016-03-30 Uttam Singh , Lin Zhang , Arun Kumar Pati

We consider a random quantum channel obtained by taking a selection of $d$ independent and Haar distributed $N$ dimensional unitaries. We follow the argument of Hastings to bound the spectral gap in terms of eigenvalues and adapt it to give…

Probability · Mathematics 2025-04-15 Sarah Timhadjelt

The dimensionality of entanglement, quantified by the Schmidt number, is a valuable resource for a wide range of quantum information processing tasks. In this work, we introduce the notion of the absolute Schmidt number, referring to states…

Quantum Physics · Physics 2026-04-06 Bivas Mallick , Saheli Mukherjee , Nirman Ganguly , A. S. Majumdar

We summarize some results of geometric measure theory concerning rectifiable sets and measures. Combined with the entropic chain rule for disintegrations (Vigneaux, 2021), they account for some properties of the entropy of rectifiable…

Information Theory · Computer Science 2023-06-02 Juan Pablo Vigneaux

We prove that the relative entropy of entanglement is additive when \emph{at least one of the two states} belongs to some specific class. We show that these classes include bipartite pure, maximally correlated, GHZ, Bell diagonal,…

Quantum Physics · Physics 2024-05-03 Roberto Rubboli , Marco Tomamichel

The design of error-correcting codes used in modern communications relies on information theory to quantify the capacity of a noisy channel to send information [1]. This capacity can be expressed using the mutual information between input…

Quantum Physics · Physics 2019-07-17 M. B. Hastings

As an application of generalised statistical mechanics, it is studied a possible route toward a consistent generalised information theory in terms of a family of non-extensive, non-parametric entropies $H^\pm_D(P)$. Unlike other proposals…

Information Theory · Computer Science 2021-03-23 Jesús Fuentes , Octavio Obregón

We determine the exact error and strong converse exponents of shared randomness-assisted channel simulation in worst case total-variation distance. Namely, we find that these exponents can be written as simple optimizations over the R\'enyi…

Information Theory · Computer Science 2024-10-10 Aadil Oufkir , Michael X. Cao , Hao-Chung Cheng , Mario Berta

We find that the asymptotic entanglement of assistance of a general bipartite mixed state is equal to the smaller of its two local entropies. Our protocol gives rise to the asymptotically optimal EPR pair distillation procedure for a given…

Quantum Physics · Physics 2007-05-23 John A. Smolin , Frank Verstraete , Andreas Winter

We describe analytical properties of the average output entropy of a quantum channel as a function of a pair (channel, input ensemble). In particular, tight semicontinuity bounds for this function with the rank/energy constraints are…

Quantum Physics · Physics 2024-04-12 M. E. Shirokov

There are processes that cannot generate entanglement but may, nevertheless, amplify entanglement already present in a system. Here, we show that a non-entangling operation can increase the Schmidt number of a quantum state only if it can…

Quantum Physics · Physics 2026-05-07 Julien Pinske , Jan Sperling , Klaus Mølmer

Statistical inference can be performed by minimizing, over the parameter space, the Wasserstein distance between model distributions and the empirical distribution of the data. We study asymptotic properties of such minimum Wasserstein…

Methodology · Statistics 2019-05-13 Espen Bernton , Pierre E. Jacob , Mathieu Gerber , Christian P. Robert

The notion of the Holevo capacity for arbitrarily constrained infinite dimensional quantum channels is introduced. It is shown that despite nonexistence of an optimal ensemble in this case it is possible to define the notion of the output…

Quantum Physics · Physics 2009-11-10 M. E. Shirokov

While the channel capacity reflects a theoretical upper bound on the achievable information transmission rate in the limit of infinitely many bits, it does not characterise the information transfer of a given encoding routine with finitely…

Neurons and Cognition · Quantitative Biology 2017-04-05 Sebastian Weichwald , Tatiana Fomina , Bernhard Schölkopf , Moritz Grosse-Wentrup

We consider entropy in Generalized Non-Signalling Theory (also known as box world) where the most common definition of entropy is the measurement entropy. In this setting, we completely characterize the set of allowed entropies for a…

Quantum Physics · Physics 2012-11-14 Josh Cadney , Noah Linden

This paper is concerned with a dissipativity theory for dynamical systems governed by linear Ito stochastic differential equations driven by random noise with an uncertain drift. The deviation of the noise from a standard Wiener process in…

Optimization and Control · Mathematics 2012-08-21 Igor G. Vladimirov , Ian R. Petersen

In this study, we generate quantum channels with random Kraus operators to typically obtain almost twirling quantum channels and quantum expanders. To prove the concentration phenomena, we use matrix Bernstein's inequality. In this way, our…

Quantum Physics · Physics 2025-06-24 Motohisa Fukuda