Probing multimode squeezing with correlation functions

Broadband multimode squeezers constitute a powerful quantum resource with promising potential for different applications in quantum information technologies such as information coding in quantum communication networks or quantum simulations in higher-dimensional systems. However, the characterization of a large array of squeezers that coexist in a single spatial mode is challenging. In this paper, we address this problem and propose a straightforward method for determining the number of squeezers and their respective squeezing strengths by using broadband multimode correlation function measurements. These measurements employ the large detection windows of the state of the art avalanche photodiodes in order to simultaneously probe the full Hilbert space of the generated state, which enables us to benchmark the squeezed states. Moreover, due to the structure of correlation functions, our measurements are not affected by losses. This is a significant advantage, since detectors with low efficiencies are sufficient. Our approach is less costly than tomographic methods relying on multimode homodyne detection, which is based on much more demanding measurement and analysis tools and appear to be impractical for large Hilbert spaces.