Optimum Testing of Multiple Hypotheses in Quantum Detection Theory

Horace P. Yuen, Robert S. Kennedy, Melvin Lax

Research output: Contribution to journalArticle

296 Scopus citations

Abstract

The problem of specifying the optimum quantum detector in multiple hypotheses testing is considered for application to optical communications. The quantum digital detection problem is formulated as a linear programming problem on an infinite-dimensional space. A necessary and sufficient condition is derived by the application of a general duality theorem specifying the optimum detector in terms of a set of linear operator equations and inequalities. Existence of the optimum quantum detector is also established. The optimality of commuting detection operators is discussed in some examples. The structure and performance of the optimal receiver are derived for the quantum detection of narrow-band coherent orthogonal and simplex signals. It is shown that modal photon counting is asymptotically optimum in the limit of a large signaling alphabet and that the capacity goes to infinity in the absence of a bandwidth limitation.

Original languageEnglish (US)
Pages (from-to)125-134
Number of pages10
JournalIEEE Transactions on Information Theory
Volume21
Issue number2
DOIs
StatePublished - Jan 1 1975

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ASJC Scopus subject areas

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences

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