The Reconstruction Problem and Weak Quantum Values

Abstract

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

To appear in J.Phys.: Math. Theor

References in corpus (5)

• Direct Measurement of the Quantum Wavefunction
• Complex weak values in quantum measurement
• Mutually Unbiased Bases for Continuous Variables
• Weak vs. approximate values in quantum state determination
• Weak values of a quantum observable and the cross-Wigner distribution

Cited by in corpus (8)

• Direct measurement of a nonlocal entangled quantum state
• Quantum optical reconstruction scheme using weak values
• Gouy phase and quantum interference with cross-Wigner functions for matter-waves
• Direct Measurement Methods of Density Matrix of an Entangled Quantum State
• The Phase Space Formulation of Time-Symmetric Quantum Mechanics, I: the Wigner Formalism
• The Optimal Pure Gaussian State Associated with Joint Position-Momentum Measurements
• Symplectic Transformations on Wigner Distributions and Time Frequency Signal Design
• Uncertainty Relations for MIMO Ambiguity Functions