相关论文: Central Limit Theorem for Bosonic Quantum Channels

This article provides an elementary introduction to Gaussian channels and their capacities. We review results on the classical, quantum, and entanglement assisted capacities and discuss related entropic quantities as well as additivity…

The Central Limit Theorem (CLT) establishes that sufficiently large sequences of independent and identically distributed random variables converge in probability to a normal distribution. This makes the CLT a fundamental building block of…

Bosonic channels describe quantum-mechanically many practical communication links such as optical, microwave, and radiofrequency. We investigate the maximum rates for the bosonic multiple access channel (MAC) in the presence of thermal…

We give analytic upper bounds to the channel capacity C for transmission of classical information in electromagnetic channels (bosonic channels with thermal noise). In the practically relevant regimes of high noise and low transmissivity,…

We determine the ultimate classical information capacity of a linear time-invariant bosonic channel with additive phase-insensitive Gaussian noise. This channel can model fiber-optic communication at power levels below the threshold for…

We study quantum channels that vary on time in a deterministic way, that is, they change in an independent but not identical way from one to another use. We derive coding theorems for the classical entanglement assisted and unassisted…

Statistical inference for non-stationary data is hindered by the failure of classical central limit theorems (CLTs), not least because there is no fixed Gaussian limit to converge to. To resolve this, we introduce relative weak convergence,…

We address the estimation of the loss parameter of a bosonic channel probed by Gaussian signals. We derive the ultimate quantum bound on precision and show that no improvement may be obtained by having access to the environment degrees of…

We develop a central limit theorem (CLT) for a non-parametric estimator of the transition matrices in controlled Markov chains (CMCs) with finite state-action spaces. Our results establish precise conditions on the logging policy under…

We review recent results on the simulation of quantum channels, the reduction of adaptive protocols (teleportation stretching), and the derivation of converse bounds for quantum and private communication, as established in PLOB [Pirandola,…

We compare two sets of multimode quantum channels acting on a finite collection of harmonic oscillators: (a) the set of linear bosonic channels, whose action is described as a linear transformation at the phase space level; and (b) Gaussian…

We find the maximum rate achievable in the private communication over a bosonic quantum channel with a fully Gaussian protocol based on optimal single-mode Gaussian measurements. This rate establishes a lower bound on the secret rate…

A pure-loss bosonic channel is a simple model for communication over free-space or fiber-optic links. More generally, phase-insensitive bosonic channels model other kinds of noise, such as thermalizing or amplifying processes. Recent work…

A longstanding open problem in quantum information theory is to find the classical capacity of an optical communication link, modeled as a Gaussian bosonic channel. It has been conjectured that this capacity is achieved by a random coding…

In this talk I first review at an elementary level a selection of central limit theorems, including some lesser known cases, for sums and maxima of uncorrelated and correlated random variables. I recall why several of them appear in…

The more than thirty years old issue of the (classical) information capacity of quantum communication channels was dramatically clarified during the last years, when a number of direct quantum coding theorems was discovered. The present…

We introduce a quantum convolution and a conceptual framework to study states in discrete-variable (DV) quantum systems. All our results suggest that stabilizer states play a role in DV quantum systems similar to the role Gaussian states…

When the underlying random variables are Gaussian, the classical Central Limit Theorem (CLT) is trivial, but the functional CLT is not. The objective of the paper is to investigate the functional CLT for stationary Gaussian processes in the…

Central limit theorems (CLTs) have a long history in probability and statistics. They play a fundamental role in constructing valid statistical inference procedures. Over the last century, various techniques have been developed in…

The long-standing conjectures of the optimality of Gaussian inputs for Gaussian channel and Gaussian additivity are solved for a broad class of covariant or contravariant Bosonic Gaussian channels (which includes in particular thermal,…