The Role of Frame Force in Quantum Detection

Abstract

A general method is given to solve tight frame optimization problems, borrowing notions from classical mechanics. In this paper, we focus on a quantum detection problem, where the goal is to construct a tight frame that minimizes an error term, which in quantum physics has the interpretation of the probability of a detection error. The method converts the frame problem into a set of ordinary differential equations using concepts from classical mechanics and orthogonal group techniques. The minimum energy solutions of the differential equations are proven to correspond to the tight frames that minimize the error term. Because of this perspective, several numerical methods become available to compute the tight frames. Beyond the applications of quantum detection in quantum mechanics, solutions to this frame optimization problem can be viewed as a generalization of classical matched filtering solutions. As such, the methods we develop are a generalization of fundamental detection techniques in radar.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 2007
Accession Number
ADA475623

Entities

People

  • Andrew Kebo
  • John Benedetto

Organizations

  • University of Maryland

Tags

DTIC Thesaurus Topics

  • Applied Mathematics
  • Computational Science
  • Detection
  • Differential Equations
  • Equations
  • Equations Of Motion
  • Hilbert Space
  • Mathematics
  • Molecular Mechanics Methods
  • Optimization
  • Physics
  • Probability
  • Quantum Cryptography
  • Quantum Mechanics
  • Real Variables
  • Signal Processing
  • Two Dimensional

Readers

  • Calculus or Mathematical Analysis
  • Image Processing and Computer Vision.
  • Operations Research

Technology Areas

  • Quantum Computing