Berlin 2005 – wissenschaftliches Programm
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Q: Quantenoptik und Photonik
Q 21: Poster Quanteneffekte
Q 21.1: Poster
Montag, 7. März 2005, 11:00–12:30, Poster HU
Hilbert’s 17th problem and the quantumness of states — •Jarek Korbicz1, Ignacio Cirac2, Jan Wehr3, and Maciej Lewenstein1 — 1Instutut fuer Theoretische Physik, Universitaet Hannover, D-30167 Hannover, Germany — 2Max-Planck Institut fuer Quantenoptik, Hans-Kopfermann Str. 1, D-85748, Garching, Germany — 3Department of Mathematics, University of Arizona, 617 N. Santa Rita Ave., Tucson, AZ 85721-0089, USA
We investigate the quantumness of states of a harmonic oscillator according to existence of the positive P-representation. We derive a family of criteria based on Bochner’s theorem, that involve averages of specific positive functions. For polynomial functions we relate these criteria to 17-th Hilbert’s problem and discuss their physical meaning. These criteria can be interpreted in terms of nonclassicality witnesses. We show that every quantum state with smooth characteristic function can be detected by a polynomial that is a sum of squares of other polynomials (sos). We also discuss the hierarchy of states regarding the degree of sos polynomial that detects them. Polynomial nonclassicality witnesses allow direct experimental detection of quantumness.