Weak Measurements As an Instance
of Non-Ideal Measurements¹

A. K. Pan* and A. Matzkin**

Laboratoire de Physique Théorique et Modélisation (CNRS Unité 8089), Université de Cergy-Pontoise,
95302 Cergy-Pontoise cedex, France

*e-mail: alok.pan@u-cergy.fr

**e-mail: alexandre.matzkin@u-cergy.fr

Received November 1, 2011; in final form, November 11, 2011; published online September 3, 2012

Abstract—We introduce weak measurements (WM) as a type of non-ideal measurement (NIM) coupling the
system and the measuring device in a specific manner involving a weak interaction followed by post-selection.
For the particular case of a WM measurement of spin, we solve the quantum dynamics for the coupled system-
meter ensemble exactly for any type of non-ideal measurement. The standard WM regime is obtained as a lim-
iting case; eccentric “semi-weak” values not only appear in other cases of NIM, but can also have a larger mag-
nitude than the usual weak values. A couple of examples comparing the merits of the WM regime and of the
exact treatment in situations of potential interest to quantum information applications are considered.

DOI: 10.1134/S1054660X12100167

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