1965/05/01 by John R. Klauder, James McKenna, Douglas G. Currie +1 · 3 citations
Computer Science · Physics and Astronomy · Mathematics · #Quantum Information and Cryptography #Quantum optics and atomic interactions #Spectral Theory in Mathematical Physics
paper · doi:10.1063/1.1704330
It is proved that every density matrix is the limit, in the sense of weak operator convergence, of a sequence of operators each of which may be represented as an integral over projection operators onto coherent states (in the sense of Glauber) with a square-integrable weight function. This result is a special case of one that holds for all operators with trace and for overcomplete families of states other than just the coherent states. We prove our more general result, at no cost of complexity, within the more general framework of continuous-representation theory. The significance of our results for representing traces of operators is indicated.