Article

# The Reconstruction Problem and Weak Quantum Values

(Impact Factor: 1.58). 12/2011; 45(11). DOI: 10.1088/1751-8113/45/11/115305
Source: arXiv

ABSTRACT

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.

### Full-text

Available from: Maurice A de Gosson, Sep 13, 2015
• Source
##### Article: Quantum optical reconstruction scheme using weak values
[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
• ##### Article: Weak Values and Born-Jordan Quantization
[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; 1508:156-161. DOI:10.1063/1.4773127
• Source
##### Article: The Phase Space Formulation of Time-Symmetric Quantum Mechanics, I: the Wigner Formalism
[Hide abstract]
ABSTRACT: Time-symmetric quantum mechanics can be described in the usual Weyl--Wigner--Moyal formalism (WWM) by using the properties of the Wigner distribution, and its generalization, the cross-Wigner distribution. The use of the latter makes clear a strongly oscillating interference between the pre- and post-selected states. This approach allows us to give explicit formulas for the state reconstruction problem, thus generalizing known results to the case of arbitrary observables. In a forthcoming paper we will extend these results to other quantization schemes.
10/2015; 4(1). DOI:10.12743/quanta.v4i1.46