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arXiv:1101.1741 · Physical Review A

Nonclassicality quasiprobability of single-photon-added thermal states

T. Kiesel, W. Vogel, Marco Bellini, Alessandro Zavatta

Published Mar 18, 2011• 65 citations
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Abstract

We report the experimental reconstruction of a nonclassicality quasiprobability for a single-photon-added thermal state. This quantity has significant negativities, which is necessary and sufficient for the nonclassicality of the quantum state. Our method exhibits several advantages compared to the reconstruction of the $P$ function, since the nonclassicality filters used in this case can regularize the quasiprobabilities as well as their statistical uncertainties. A priori assumptions about the quantum state are therefore not necessary. We also demonstrate that, in principle, our method is not limited by small quantum efficiencies.

DOI
10.1103/physreva.83.032116

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We report the experimental reconstruction of a nonclassicality quasiprobability for a single-photon-added thermal state. This quantity has significant negativities, which is necessary and sufficient for the nonclassicality of the quantum state. Our method exhibits several advantages compared to the reconstruction of the PPP function, since the nonclassicality filters used in this case can regularize the quasiprobabilities as well as their statistical uncertainties. A priori assumptions about the quantum state are therefore not necessary. We also demonstrate that, in principle, our method is not limited by small quantum efficiencies.
A quantum state is nonclassical if its Glauber-Sudarshan PPP function fails to be interpreted as a probability density. This quantity is often highly singular, so that its reconstruction is a demanding task. Here we present the experimental determination of a well-behaved PPP function showing negativities for a single-photon-added thermal state. This is a direct visualization of the original definition of nonclassicality. The method can be useful under conditions for which many other signatures of nonclassicality would not persist.
Nonclassicality filters provide a universal method to visualize the nonclassicality of arbitrary quantum states of light through negativities of a regularized Glauber-Sudarshan PPP function, also denoted as nonclassicality quasiprobability. Such filters are introduced and analyzed for optimizing the experimental certification of nonclassical effects. An analytic filter is constructed which preserves the full information on the quantum state. For balanced homodyne detection, the number of data points is analyzed to get the negativities of the nonclassicality quasiprobability with high statistical significance. The method is applied to different scenarios, such as phase-randomized squeezed vacuum states, single-photon-added thermal states, and heralded state engineering with array detectors. The generalization to visualize quantum correlations of multimode radiation fields is also considered.
Negative probability values have been widely employed as an indicator of the nonclassicality of quantum systems. Known as a quasiprobability distribution, they are regarded as a useful tool that provides significant insight into the underlying fundamentals of quantum theory when compared to the classical statistics. However, in this approach, an operational interpretation of these negative values with respect to the definition of probability---the relative frequency of occurred event---is missing. An alternative approach is therefore considered where the quasiprobability operationally reveals the negativity of measured quantities. We here present an experimental realization of the operational quasiprobability, which consists of sequential measurements in time. To this end, we implement two sets of polarization measurements of single photons. We find that the measured negativity can be interpreted in the context of selecting measurements, and it reflects the nonclassical nature of photons. Our results suggest a new operational way to unravel the nonclassicality of photons in the context of measurement selection.
We show the experimental observation of quantum states of light exhibiting nonclassical features obtained by single photon excitation of a thermal state. Such single-photon-added thermal states are the result of the single action of the creation operator on a mixed state that can be fully described classically. They show different degree of nonclassicality depending on the mean photon number of the original thermal state. The generated state is characterized by means of ultra-fast homodyne detection which allows us to reconstruct its density matrix and Wigner function by quantum tomography. We demonstrate the nonclassical behavior of single-photon added thermal states by an analysis of the negativity of the Wigner function.
In spite of its fundamental importance in quantum science and technology, the experimental certification of nonclassicality is still a challenging task, especially in realistic scenarios where losses and noise imbue the system. Here, we present the first experimental implementation of the recently introduced phase-space inequalities for nonclassicality certification, which conceptually unite phase-space representations with correlation conditions. We demonstrate the practicality and sensitivity of this approach by studying nonclassicality of a family of noisy and lossy quantum states of light. To this end, we experimentally generate single-photon-added thermal states with various thermal mean photon numbers and detect them at different loss levels. Based on the reconstructed Wigner and Husimi Q functions, the inequality conditions detect nonclassicality despite the fact that the involved distributions are nonnegative, which includes cases of high losses (93%) and cases where other established methods do not reveal nonclassicality. We show the advantages of the implemented approach and discuss possible extensions that assure a wide applicability for quantum science and technologies.