Related papers: Norms of quantum Gaussian multi-mode channels
We define a new family of codes for symmetric classical-quantum channels and establish their optimality. To this end, we extend the classical notion of generalized perfect and quasi-perfect codes to channels defined over some finite…
We study the capacity of the power-constrained additive Gaussian channel with an entropy constraint at the input. In particular, we characterize this capacity in the low signal-to-noise ratio regime at small entropy. This follows as a…
In this paper we consider the computation of channel capacity for ergodic multiple-input multiple-output channels with additive white Gaussian noise. Two scenarios are considered. Firstly, a time-varying channel is considered in which both…
We calculate the quantum Cram\'er--Rao bound for the sensitivity with which one or several parameters, encoded in a general single-mode Gaussian state, can be estimated. This includes in particular the interesting case of mixed Gaussian…
We calculate the quantum Cram\'er--Rao bound for the sensitivity with which one or several parameters, encoded in a general single-mode Gaussian state, can be estimated. This includes in particular the interesting case of mixed Gaussian…
Optimal signaling for secrecy rate maximization in Gaussian MIMO wiretap channels is considered. While this channel has attracted a significant attention recently and a number of results have been obtained, including the proof of the…
We quantify, uniformly over time and with high probability, the discrepancy between the predictions of a two-layer neural network trained by stochastic gradient descent (SGD) and their mean-field limit, for quadratic loss and ridge…
In this paper we will demonstrate that any compact quantum group can be used as symmetry groups for quantum channels, which leads us to the concept of covariant channels. We, then, unearth the structure of the convex set of covariant…
The purpose of this work is to extend the result of previous papers quant-ph/9611023, quant-ph/9703013 to quantum channels with additive constraints onto the input signal, by showing that the capacity of such channel is equal to the…
We present a new application of harmonic analysis to quantum information by constructing intriguing classes of quantum channels stemming from specific representations of multiplier algebras over locally compact groups $G$. Beginning with a…
Motivated by the definition of the Gowers uniformity norms, we introduce and study a wide class of norms. Our aim is to establish them as a natural generalization of the $L_p$ norms. We shall prove that these normed spaces share many of the…
This paper explores the two-user Gaussian interference channel through the lens of a natural deterministic channel model. The main result is that the deterministic channel uniformly approximates the Gaussian channel, the capacity regions…
The current quantum resource theory for Gaussian steering for continuous-variable systems is flawed and incomplete. Its primary shortcoming stems from an inadequate comprehension of the architecture of Gaussian channels transforming…
In recent years, infinite-dimensional methods have been introduced for the Gaussian channels estimation. The aim of this paper is to study the application of similar methods to Poisson channels. In particular we compute the Bayesian…
We prove an entropic uncertainty relation for two quantum channels, extending the work of Frank and Lieb for quantum measurements. This is obtained via a generalized strong super-additivity (SSA) of quantum entropy. Motivated by Petz's…
Entropy comparison inequalities are obtained for the differential entropy $h(X+Y)$ of the sum of two independent random vectors $X,Y$, when one is replaced by a Gaussian. For identically distributed random vectors $X,Y$, these are closely…
Normative modeling has recently been proposed as an alternative for the case-control approach in modeling heterogeneity within clinical cohorts. Normative modeling is based on single-output Gaussian process regression that provides coherent…
We explore complementarity between output and environment of a quantum channel (or, more generally, CP map), making an observation that the output purity characteristics for complementary CP maps coincide. Hence, validity of the…
We consider the problem of selecting $k_t \times k_r$ antennas from a Gaussian MIMO channel with $n_t \times n_r$ antennas, where $k_t \leq n_t$ and $k_r \leq n_r$. We prove the following two results that hold universally, in the sense that…
In this paper, we formularize a method for randomizing quantum states with respect to the Schatten $p$-norm ($p\ge1$). Our theorem includes the Lemma 2.2 of Hayden and Winter [Commun. Math. Phys. {\bf 284}, 263--280 (2008)] for the norm…