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arXiv:1711.10962 · Physical Review Letters

Incomplete Detection of Nonclassical Phase-Space Distributions

Martin Bohmann, Johannes Tiedau, Tim J. Bartley, Jan Sperling, Christine Silberhorn, W. Vogel

Published Feb 9, 2018• 32 citations
arXivHTMLPDF

Abstract

We implement the direct sampling of negative phase-space functions via unbalanced homodyne measurement using click-counting detectors. The negativities significantly certify nonclassical light in the high-loss regime using a small number of detectors which cannot resolve individual photons. We apply our method to heralded single-photon states and experimentally demonstrate the most significant certification of nonclassicality for only two detection bins. By contrast, the frequently applied Wigner function fails to directly indicate such quantum characteristics for the quantum efficiencies present in our setup without applying additional reconstruction algorithms. Therefore, we realize a robust and reliable approach to characterize nonclassical light in phase space under realistic conditions.

DOI
10.1103/physrevlett.120.063607

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We implement the direct sampling of negative phase-space functions via unbalanced homodyne measurement using click-counting detectors. The negativities significantly certify nonclassical light in the high-loss regime using a small number of detectors which cannot resolve individual photons. We apply our method to heralded single-photon states and experimentally demonstrate the most significant certification of nonclassicality for only two detection bins. By contrast, the frequently applied Wigner function fails to directly indicate such quantum characteristics for the quantum efficiencies present in our setup without applying additional reconstruction algorithms. Therefore, we realize a robust and reliable approach to characterize nonclassical light in phase space under realistic conditions.
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Driven by single photon detection requirements, the theory of arrays of off-on detectors has been developed and applied. However, for a comprehensive characterization of nonclassicality, one also needs phase sensitive properties. This missing link is introduced with the derived theory of phase sensitive click counting measurements. It unifies the balanced homodyne detection for high intensities with the click detection in the few-photon regime. We formulate a hierarchy of nonlinear squeezing conditions to probe quantum effects beyond standard squeezing. Imperfections stemming from fluctuations, detector efficiency, and dark count rates are considered. Experimentally accessible sampling formulas are given. Our theory paves the way towards novel applications of light in quantum metrology.
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.
States with negative Wigner functions constitute a fundamental nonclassical resource underlying quantum advantage. However, their experimental certification typically relies on reconstructing the full phase-space distribution, resulting in a prohibitive measurement overhead for arbitrary quantum states. In this letter, we overcome this limitation by introducing Wigner moments, a family of global phase-space quantities that admit an exact multicopy realization as parity expectation values, and are therefore directly measurable from only a modest number of state copies. This operational correspondence enables systematic hierarchies of detection criteria together with experimentally accessible lower bounds on the logarithmic Wigner negativity, and constitutes a genuine measure of nonclassicality. Numerical benchmarking of our protocol reveals a substantial reduction in copy budget relative to conventional Wigner tomography, establishing Wigner moments as an efficient framework for certifying continuous-variable quantum resources such as genuine multipartite entanglement.
The representation of quantum states via phase-space functions constitutes an intuitive technique to characterize light. However, the reconstruction of such distributions is challenging as it demands specific types of detectors and detailed models thereof to account for their particular properties and imperfections. To overcome these obstacles, we derive and implement a measurement scheme that enables a reconstruction of phase-space distributions for arbitrary states whose functionality does not depend on the knowledge of the detectors, thus defining the notion of detector-agnostic phase-space distributions. Our theory presents a generalization of well-known phase-space quasiprobability distributions, such as the Wigner function. We implement our measurement protocol, using state-of-the-art transition-edge sensors without performing a detector characterization. Based on our approach, we reveal the characteristic features of heralded single- and two-photon states in phase space and certify their nonclassicality with high statistical significance.
Measures of quantum properties are essential to understanding the fundamental differences between quantum and classical systems as well as quantifying resources for quantum technologies. Here, two broad classes of bosonic phase-space functions, which are filtered versions of the Glauber-Sudarshan P function, are compared with regard to their ability to uncover nonclassical effects of light through their negativities. Gaussian filtering of the P function yields the family of s-parametrized quasiprobabilities, while more powerful regularized nonclassicality quasiprobabilities are obtained by non-Gaussian filtering. A method is proposed to directly sample such phase-space functions for the restricted case of phase-independent quantum states from balanced homodyne measurements. This overcomes difficulties of previous approaches that manually append uniformly distributed optical phases to the measured quadrature data. We experimentally demonstrate this technique for heralded single- and two-photon states using balanced homodyne detection with varying efficiency. The s-parametrized quasiprobabilities, which can be directly sampled, are non-negative for detection efficiencies below 0.5. By contrast, we show that significant negativities of non-Gaussian filtered quasiprobabilities uncover nonclassical effects for arbitrarily low efficiencies.