  In a seminal work, Aharonov, Albert, and Vaidman showed that by having a weak
interaction between a system and a detecting apparatus, the average output of
the latter could be much larger than the maximum eigenvalue of the observed
quantity (times the amplification factor). This does not always happen,
however: the observed system must subsequently undergo a second measurement, on
the output of which the result of the first one is conditioned. This procedure
is known as postselection. On the other hand, linear response theory describes
how the observables of a quan- tum system change upon perturbation by a weak
classical external force. In a measurement, the measured system applies a
generalized force to the measuring apparatus, leading to an observable change
in the latter. It appears natural, then, to unify the treatment of weak
measurements with an extended version of linear response theory that accounts
for a force introduced by an external quantum system. Here, we show how the
postselection introduces a complex force term and we provide a modified Kubo
formula working in the non-linear regime.
