, Volume 10, Issue 3, pp 227-238

First online:

New light on the optical equivalence theorem and a new type of discrete diagonal coherent state representation

  • N MukundaAffiliated withCentre for Theoretical Studies, Indian Institute of Science
  • , E C G SudarshanAffiliated withCentre for Theoretical Studies, Indian Institute of Science

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In many instances we find it advantageous to display a quantum optical density matrix as a generalized statistical ensemble of coherent wave fields. The weight functions involved in these constructions turn out to belong to a family of distributions, not always smooth functions. In this paper we investigate this question anew and show how it is related to the problem of expanding an arbitrary state in terms of an overcomplete subfamily of the overcomplete set of coherent states. This provides a relatively transparent derivation of the optical equivalence theorem. An interesting by-product is the discovery of a new class of discrete diagonal representations.


Optical equivalence theorem coherent states overcomplete family of states discrete diagonal representation