Weak Values, the Reconstruction Problem, and the Uncertainty Principle

Emergent Quantum Mechanics 2015

De Gosson, Charlyne^1 ; De Gosson, Maurice^1

Universität Wien, NuHAG, Fakultät für Mathematik, Wien

A-1090, Austria^1

关键词: Ancillary state;    Hardy uncertainty principle;    Reconstruction problems;    Uncertainty principles;    Von Neumann measurement;    Weak measurements;    Weak values;    Wigner transforms;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/701/1/012011/pdf
DOI  :  10.1088/1742-6596/701/1/012011

来源: IOP

【 摘 要 】

Closely associated with the notion of weak value is the problem of reconstructing the post-selected state: this is the so-called reconstruction problem. We show that the reconstruction problem can be solved by inversion of the cross-Wigner transform, using an ancillary state. We thereafter show, using the multidimensional Hardy uncertainty principle, that maximally concentrated cross-Wigner transforms corresponds to the case where a weak measurement reduces to an ordinary von Neumann measurement.