On the moment limit of quantum observables, with an application to the balanced homodyne detection

J. Kiukas*, P. Lahti

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

11 Citations (SciVal)

Abstract

We consider the moment operators of the observable (i.e. a semispectral measure or POM) associated with the balanced homodyne detection statistics, whilst paying attention to the correct domains of these unbounded operators. We show that the high amplitude limit, when performed on the moment operators, actually determines uniquely the entire statistics of a rotated quadrature amplitude of the signal field, thereby verifying the usual assumption that the homodyne detection achieves a measurement of that observable. We also consider, in a general setting, the possibility of constructing a measurement of a single quantum observable from a sequence of observables by taking the limit on the level of moment operators of these observables. In this context, we show that under some natural conditions (each of which is satisfied by the homodyne detector example), the existence of the moment limits ensures that the underlying probability measures converge weakly to the probability measures of the limiting observable. The moment approach naturally requires that the observables be determined by their moment operator sequences (which does not automatically happen), and it turns out, in particular, that this is the case for the balanced homodyne detector.

Original languageEnglish
Pages (from-to)1175-1198
Number of pages24
JournalJournal of Modern Optics
Volume55
Issue number7
DOIs
Publication statusPublished - 12 May 2008
Externally publishedYes

Keywords

  • Balanced homodyne detection
  • High amplitude limit
  • Moment problem
  • Operator integral
  • Positive operator measure

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