# Quantum Limits on the Information Carried by Electromagnetic Radiation

Tuesday, November 14, 2017 - 4:00pm to Wednesday, November 15, 2017 - 3:55pm

### Event Calendar Category

LIDS Seminar Series

### Speaker Name

Massimo Franceschetti

### Affiliation

University of California, San Diego

32-141

### Abstract

In many practical applications information is conveyed by means of electromagnetic radiation and a natural question concerns the fundamental limits of this process. Identifying information with entropy, one can ask about the maximum amount of entropy associated to the propagating wave.

The standard statistical physics approach to compute entropy is to take the logarithm of the number of possible energy states of a system. Since any continuum field can assume an uncountably infinite number of energy configurations, the approach underlying any finite entropy calculation must also necessarily include some grouping of states together in a procedure known as coarse graining or, in information-theoretic parlance, signal quantization. The problem then reduces to counting the eigenstates of the Hamiltonian of the quantum wave field.

In this talk, we examine the relationship between entropy computations in a statistical physics and an information-theory context. In the latter context, rather than attempting to directly count the number of energy eigenstates of the quantum wave field, we constrain the geometry of the signal space and decompose the waveform into a minimum number of orthogonal basis modes. We then ask how many bits are required to represent any waveform in the space spanned by this optimal representation with a minimum quantized energy error. We show that for scalar quantization this entropy computation is completely analogous to the one for the number state channel of statistical physics, and it has the attractive feature that the complexity of state counting is now replaced by the geometric problem of optimally covering the signal space by high-dimensional boxes, whose size is lower bounded by quantum constraints. For bandlimited radiation in a three-dimensional space, using this approach we can recover the Bekenstein entropy bound on the largest amount of information that can be radiated from a sphere of given radius. We also compare results with black body radiation occurring over an infinite spectrum of frequencies and along the way we provide some new results on the asymptotic dimensionality and $\epsilon$-entropy of bandlimited, square-integrable signals.

### Biography

Massimo Franceschetti received the Laurea degree (with highest honors) in computer engineering from the University of Naples, Naples, Italy, in 1997, the M.S. and Ph.D. degrees in electrical engineering from the California Institute of Technology, Pasadena, CA, in 1999, and 2003, respectively. He is Professor of Electrical and Computer Engineering at the University of California at San Diego (UCSD). Before joining UCSD, he was a postdoctoral scholar at the University of California at Berkeley for two years. His research interests are in physical and information-based foundations of communication and control systems. He was awarded the C. H. Wilts Prize in 2003 for best doctoral thesis in electrical engineering at Caltech, the S.A. Schelkunoff Award in 2005 for best paper in the IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, a National Science Foundation (NSF) CAREER award in 2006, an Office of Naval Research (ONR) Young Investigator Award in 2007, the IEEE Communications Society Best Tutorial Paper Award in 2010, and the IEEE Control theory society Ruberti young researcher award in 2012.