Abstract
We devise a method to certify nonclassical features via correlations of phase-space distributions by unifying the notions of quasiprobabilities and matrices of correlation functions. Our approach complements and extends recent results that were based on Chebyshev's integral inequality \cite{BA19}. The method developed here correlates arbitrary phase-space functions at arbitrary points in phase space, including multimode scenarios and higher-order correlations. Furthermore, our approach provides necessary and sufficient nonclassicality criteria, applies to phase-space functions beyonds-parametrized ones, and is accessible in experiments. To demonstrate the power of our technique, the quantum characteristics of discrete- and continuous-variable, single- and multimode, as well as pure and mixed states are certified only employing second-order correlations and Husimi functions, which always resemble a classical probability distribution. Moreover, nonlinear generalizations of our approach are studied. Therefore, a versatile and broadly applicable framework is devised to uncover quantum properties in terms of matrices of phase-space distributions.
Highlights
Telling classical and quantum features of a physical system apart is a key challenge in quantum physics
The notion of nonclassicality provides the basis for many applications in photonic quantum technology and quantum information [1, 2, 3, 4, 5]
Each of the resulting modes is measured with a detector or detection scheme based on photon absorption, being described by a positive operatorvalued measure (POVM) which is diagonal in the photon-number representation [79]
Summary
Telling classical and quantum features of a physical system apart is a key challenge in quantum physics. Examples in optics are photon anti-bunching [36, 37, 38] and subPoissonian photon-number distributions [39, 40], using intensity correlations, as well as various squeezing criteria, being based on field-operator correlations [41, 42, 43, 44] They can follow, for instance, from applying Cauchy-Schwartz inequalities [45] and uncertainty relations [46], as well as from other violations of classical bounds [47, 48, 49]. These first demonstrations of combining phasespace distributions and matrices of moments are still restricted to rather specific scenarios In this contribution, we formulate a general framework for uncovering quantum features through correlations in phase-space matrices which unifies these two fundamental approaches to characterizing quantum systems.
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