  We study quantum state tomography, entanglement detection, and channel noise
reconstruction of propagating quantum microwaves via dual-path methods. The
presented schemes make use of the following key elements: propagation channels,
beam splitters, linear amplifiers, and field quadrature detectors. Remarkably,
our methods are tolerant to the ubiquitous noise added to the signals by
phase-insensitive microwave amplifiers. Furthermore, we analyze our techniques
with numerical examples and experimental data, and compare them with the scheme
developed in Eichler $et$ $al$ (2011 Phys. Rev. Lett. 106 220503; 2011 Phys.
Rev. Lett. 107 113601), based on a single path. Our methods provide key toolbox
components that may pave the way towards quantum microwave teleportation and
communication protocols.
