Quantumness of states [Elektronische Ressource] : from positive P-representations to entanglement tests / von Jarosław Korbicz

Quantumness of States:From positiveP-representationstoEntanglement TestsVon der Fakult˜at fur˜ Mathematik und Physikder Universit˜at Hannoverzur Erlangung des GradesDoktor der NaturwissenschaftenDr. rer. nat.genehmigte DissertationvonDipl.-Phys. Jarosˆlaw Korbiczgeboren am 07. October 1976 in KievReferent: Prof. Dr. M. LewensteinKorreferent: Prof. Dr. O. LechtenfeldTag der Promotion: 16.06.2006To my wife AgnieszkaDo we not do better to recognize that what we call existenceconsists of countably many iron posts of observation betweenwhich we flll in by an elaborate papier-ma^ch¶e construction ofimagination and theory?John Archibald WheelerAbstractWe address the general problem of characterization of states of a quantum systemthat do not have classical analogs.At flrst, we study the long standing problem of characterization of quantum-ness of states of simple mechanical systems. Using the Galuber-Sudarshan P-representation and the techniques of Fourier transform, we derive a novel familyof classicality criteria. For a very broad class of states, these criteria are related toHilbert’s 17th problem: a generic non-classical state can be detected by a polyno-mial that is a sum of squares of other polynomials. This leads to a natural hierarchyof states regarding their degree of quantumness. Our criteria have the physicalmeaning of generalized squeezing conditions.