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For the sake of example, we consider a specific weak amplification scheme [@brunner2010], depicted in Fig. 1, which has been recently demonstrated experimentally [@xu_guo2013; @salazar2014]. It aims at measuring very small temporal delays $\tau$, or correspondingly tiny phase changes [@strubi2013], with the help of optical pulses of much larger duration. We consider this specific case because it contains the main ingredients of a typical WVA scheme, explained below, and it allows to derive analytical expressions of all quantities involved, which facilitates the analysis of main results. Moreover, the scheme makes use of linear optics elements only and also works with large-bandwidth partially-coherent light [@li_guo2011].

In general, a WVA scheme requires three main ingredients: a) the consideration of two subsystems (here two degrees of freedom: the polarisation and the spectrum of an optical pulse) that are weakly coupled (here we make use of a polarisation-dependent temporal delay that is introduced with the help of a Michelson interferometer); b) the [*pre-selection*]{} of the input state of both subsystems; and c) the [*post-selection*]{} of the state in one of the subsystems (the state of polarisation) and the measurement of the state of the remaining subsystem (the spectrum of the pulse). With 