The Reconstruction Problem and Weak Quantum Values

Journal of Physics A Mathematical and Theoretical (Impact Factor: 1.58). 12/2011; 45(11). DOI: 10.1088/1751-8113/45/11/115305
Source: arXiv


Quantum Mechanical weak values are an interference effect measured by the
cross-Wigner transform W({\phi},{\psi}) of the post-and preselected states,
leading to a complex quasi-distribution {\rho}_{{\phi},{\psi}}(x,p) on phase
space. We show that the knowledge of {\rho}_{{\phi},{\psi}}(z) and of one of
the two functions {\phi},{\psi} unambiguously determines the other, thus
generalizing a recent reconstruction result of Lundeen and his collaborators.

Download full-text


Available from: Maurice A de Gosson, Sep 13, 2015
38 Reads
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: A quantum state contains the maximal amount of information available for a given quantum system. In this paper we use weak-value expressions to reconstruct quantum states of continuous-variable systems in the quantum optical domain. The role played by postselecting measured data will be particularly emphasized in the proposed setup, which is based on an interferometer just using simple homodyne detection.
    Physical Review A 11/2012; 86(5). DOI:10.1103/PhysRevA.86.052110 · 2.81 Impact Factor
  • [Show abstract] [Hide abstract]
    ABSTRACT: We study the notion of weak value of a quantum observable introduced by Aharonov from the point of view of the Born-Jordan quantization scheme. While both quantizations agree for observables of the type "kinetic energy plus potential" they lead to different weak values for general quantum observables. Weak measurements could thus provide an experimental test for the determination of the correct quantization scheme.
    12/2012; DOI:10.1063/1.4773127