Abstract
We derive a theoretical framework for the experimental certification of non-Gaussian features of quantum states using double homodyne detection. We rank experimental non-Gaussian states according to the recently defined stellar hierarchy and we propose practical Wigner negativity witnesses. We simulate various use-cases ranging from fidelity estimation to witnessing Wigner negativity. Moreover, we extend results on the robustness of the stellar hierarchy of non-Gaussian states. Our results illustrate the usefulness of double homodyne detection as a practical measurement scheme for retrieving information about continuous variable quantum states.
Highlights
Recent years have witnessed many developments that are paving the road towards quantum technologies [1,2,3,4]
CV quantum states are represented in phase space using quasiprobability distributions [11], such as GlauberSudarshan, Wigner, or Husimi functions
Quantum states are split into two main categories according to the shape of their representation in phase space: Gaussian
Summary
Recent years have witnessed many developments that are paving the road towards quantum technologies [1,2,3,4]. We provide a complementary approach for certifying the presence of non-Gaussian features of quantum states, namely stellar rank and Wigner negativity, based on double homodyne detection [30,31] This detection scheme is directly connected to the Q function, which can be exploited for retrieving information about CV quantum states [32] and for the verification of Boson Sampling output states [33,34]. We provide a multimode generalization of this result (Appendix E); (ii) a detailed statistical analysis (see Appendix A) using both experimental and simulated data and showing the reliability of our methods for the certification of non-Gaussian properties of quantum states; and (iii) the introduction of reliable Wigner-negativity witnesses based on similar techniques. Our results show that certification of high-order non-Gaussian features is within the reach of current optical experiments and is not prohibited by an unreachable amount of samples needed: with a realistic amount of loss and an achievable number of measurements, we can extract stellar rank and Wigner negativity with a high degree of confidence
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