# Dual-path state reconstruction scheme for propagating quantum microwaves and detector noise tomography 

E. P. Menzel, 1, 2, ∗ F. Deppe, 1, 2 M. Mariantoni, 1, 2, † M. ´ A. Araque Caballero, 1, 2 

A. Baust, 1, 2 T. Niemczyk, 1, 2 E. Hoffmann, 1, 2 A. Marx, 1 E. Solano, 3, 4 and R. Gross 1, 2 

$^{1}$Walther-Meißner-Institut, Bayerische Akademie der Wissenschaften, D-85748 Garching, Germany 

$^{2}$Physik-Department, Technische Universit¨ at M¨ unchen, D-85748 Garching, Germany 

$^{3}$Departamento de Qu´ımica F´ısica, Universidad del Pa´ıs Vasco - Euskal Herriko Unibertsitatea, Apdo. 644, 48080 Bilbao, Spain 

$^{4}$IKERBASQUE, Basque Foundation for Science, 48011 Bilbao, Spain 

(Dated: October 11, 2018) 

## Abstract 

Quantum state reconstruction involves measurement devices that are usually described by ide- alized models, but not known in full detail in experiments. For weak propagating microwaves, the detection process requires linear amplifiers which obscure the signal with random noise. Here, we introduce a theory which nevertheless allows one to use these devices for measuring all quadra- ture moments of propagating quantum microwaves based on cross-correlations from a dual-path amplification setup. Simultaneously, the detector noise properties are determined, allowing for tomography. We demonstrate the feasibility of our novel concept by proof-of-principle experiments with classical mixtures of weak coherent microwaves. 

PACS numbers: 03.65.Wj,07.57.Kp 

