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arXiv:1207.6097 · Physical Review A

Complete nonclassicality test with a photon-number-resolving detector

T. Kiesel, W. Vogel

Published Sep 21, 2012• 14 citations
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Abstract

We present a method for the experimental measurement of nonclassicality witnesses and demonstrate its application. Our proposal requires only the coherent displacement of the initial state, which can be achieved by overlapping the latter with a coherent state at a beam splitter, and subsequent photon-number-resolved detection. This setup allows a complete test of nonclassicality of an arbitrary quantum state. The role of the quantum efficiency as well as statistical and systematic uncertainties are discussed. Finally, the scheme is demonstrated for a realistic example.

DOI
10.1103/physreva.86.032119

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Abstract Experimentally certifying the nonclassicality of quantum states in a reliable and efficient way is a challenge that remains both fundamental and daunting. Despite decades of topical research, techniques that can exploit optimally the information available in a given experimental setup are lacking. Here, we introduce a different paradigm to tackle these challenges, that is both directly applicable to experimental realities, and extendible to a wide variety of circumstances. We demonstrate that Klyshko’s criteria, which remained a primary approach to tackle nonclassicality for the past 20 years, is a special case of a much more general class of nonclassicality criteria. We provide both analytical results and numerical evidence for the optimality of our approach in several different scenarios of interest for trapped-ion, superconducting circuits, optical and optomechanical experiments with photon-number resolving detectors. This work represents a significant milestone towards a complete characterisation of the nonclassicality detectable from the limited knowledge scenarios faced in experimental implementations.
Assessing whether a quantum state $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\rho}}$ is nonclassical (i.e., incompatible with a mixture of coherent states) is a ubiquitous question in quantum optics, yet a nontrivial experimental task because many nonclassicality witnesses are nonlinear in $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\rho}}$. In particular, if we want to witness or measure the nonclassicality of a state by evaluating its quadrature coherence scale, this a priori requires full state tomography. Here, we provide an experimental procedure for directly accessing this quantity with a simple linear interferometer involving two replicas (independent and identical copies) of the state $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\rho}}$ supplemented with photon-number-resolving measurements. This finding, which we interpret as an extension of the Hong-Ou-Mandel effect, illustrates the wide applicability of the multicopy interferometric technique in order to circumvent state tomography in quantum optics.