DocumentCode :
2945944
Title :
Weighted Norms of Ambiguity Functions and Wigner Distributions
Author :
Jung, Peter
Author_Institution :
Fraunhofer German-Sino Lab for Mobile Commun., Heinrich-Hertz-Inst.
fYear :
2006
fDate :
9-14 July 2006
Firstpage :
1519
Lastpage :
1523
Abstract :
In this article new bounds on weighted p-norms of ambiguity functions and Wigner functions are derived. Such norms occur frequently in several areas of physics and engineering. In pulse optimization for Weyl-Heisenberg signaling in wide-sense stationary uncorrelated scattering channels for example it is a key step to find the optimal waveforms for a given scattering statistics which is a problem also well known in radar and sonar waveform optimizations. The same situation arises in quantum information processing and optical communication when optimizing pure quantum states for communicating in bosonic quantum channels, i.e. find optimal channel input states maximizing the pure state channel fidelity. Due to the non-convex nature of this problem the optimum and the maximizers itself are in general difficult find, numerically and analytically. Therefore upper bounds on the achievable performance are important which will be provided by this contribution. Based on a result due to E. Lieb, the main theorem status a new upper bound which is independent of the waveforms and becomes tight only for Gaussian weights and waveforms. A discussion of this particular important case, which tighten recent results on Gaussian quantum fidelity and coherent states, will be given. Another bound is presented for the case where scattering is determined only by some arbitrary region in phase space
Keywords :
Gaussian channels; light scattering; optical communication; quantum communication; telecommunication signalling; Gaussian quantum fidelity; Gaussian weights; Weyl-Heisenberg signaling; Wigner functions; ambiguity functions; bosonic quantum channels; channel fidelity; optical communication; pulse optimization; quantum information processing; scattering statistics; weighted p-norms; wide-sense stationary uncorrelated scattering channels; Information processing; Optical fiber communication; Optical pulses; Optical scattering; Particle scattering; Physics; Radar scattering; Sonar; Statistics; Upper bound;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
Information Theory, 2006 IEEE International Symposium on
Conference_Location :
Seattle, WA
Print_ISBN :
1-4244-0505-X
Electronic_ISBN :
1-4244-0504-1
Type :
conf
DOI :
10.1109/ISIT.2006.262122
Filename :
4036221
Link To Document :
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