1202.5148 (Bengt E Y Svensson)

New wine in old bottles: Quantum measurement - direct, indirect, weak -
with some applications    [PDF]

Bengt E Y Svensson

In this, partly pedagogical review, I attempt to give a self-contained
overview of the basis of (non-relativistic) QM measurement theory expressed in
density matrix formalism. The focus is on applications to the theory of weak
measurement, as developed by Aharonov and Vaidman and their collaborators.
Their development of weak measurement combined with what they call
'post-selection' - judiciously choosing not only the initial state of a system
('pre-selection') but also its final state - has received much attention
recently. Not the least has it opened up new, fruitful experimental vistas,
like novel approaches to amplification. But the approach has also attached to
it some air of mystery. I will attempt to 'de-mystify' it by showing that
(almost) all results can be derived in a straight-forward way from conventional
QM. Among other things, I develop the formalism not only to first order but
also to second order in the weak interaction responsible for the measurement.
This also allows me to derive, more or less as a by-product, the master
equation for the density matrix of an open system in interaction with an
environment. One particular application I shall treat of the weak measurement
is the so called Leggett-Garg inequalities, a k a 'Bell inequalities in time'.
I also give an outline, even if rough, of some of the ingenious experiments
that the work by Aharonov, Vaidman and collaborators has inspired. If anything
is magic in the weak measurement + post-selection approach, it is the
interpretation of the so called weak value of an observable. Is it a bona fide
property of the system considered? I have no answer to this question; I shall
only exhibit the pros and cons of the proposed interpretation.

View original: http://arxiv.org/abs/1202.5148