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Physical Review A

Hierarchy of feasible nonclassicality criteria for sources of photons

Radim Filip, Lukáš Lachman

Published Oct 15, 2013• 30 citations
Publisher

Abstract

We present an ab-initio derivation of a hierarchy of efficient nonclassicality criteria for sources of photons. The operational criteria are explicitly proposed for the linear optical multiport and feasible multiplexed single-photon detectors. The lowest criterion is equivalent to the frequently used ${g}^{(2)}(0)$ autocorrelation measurement testing the anticorrelation effect of photons. We also derive a hierarchy of criteria for the detectors capable to at least partially estimate photon-number distribution. We prove the usefulness of both hierarchies to detect the nonclassical states from the noisy multimode single-photon sources and the nonclassical states from the multiphoton sources.

DOI
10.1103/physreva.88.043827

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We present an ab-initio derivation of a hierarchy of efficient nonclassicality criteria for sources of photons. The operational criteria are explicitly proposed for the linear optical multiport and feasible multiplexed single-photon detectors. The lowest criterion is equivalent to the frequently used g(2)(0){g}^{(2)}(0)g(2)(0) autocorrelation measurement testing the anticorrelation effect of photons. We also derive a hierarchy of criteria for the detectors capable to at least partially estimate photon-number distribution. We prove the usefulness of both hierarchies to detect the nonclassical states from the noisy multimode single-photon sources and the nonclassical states from the multiphoton sources.
Abstract Single photon sources are necessary for optical quantum technology. The nonclassicality of emitted single photons manifests itself in diverse experiments and applications. The applications already require different nonclassical aspects of single photons, however, a suitable hierarchy of criteria is missing. We propose variable experimental tests, based on adjustable linear optical networks and single photon detectors, giving a hierarchy of such nonclassicality criteria. The hierarchy goes beyond Hanbury–Brown–Twiss test of photon antibunching and allows us to compare faithfully quality and performance of single photon sources via their nonclassical properties.
We ab initio derive quantum nonclassicality and non-Gaussianity criteria for realistic single-photon sources and discuss the robustness of these quantum features in attenuating quantum channel. The derivation based only on assumptions about the structure of the detector is performed for standard autocorrelation measurement with single-photon detectors. Using both the criteria, we compare the robustness of quantum features of realistic single-photon states with the Poissonian and thermal background noise and discuss a difference between the impact of the multimode structure of thermal noise and truly Poissonian noise.
We address the problem of constructing witnesses for nonclassical light that are applicable in state-of-the-art photon-counting devices. The key ingredient for the criteria we derive are generalized and directly measurable counting statistics and matrices of counting moments. Beyond common criteria, we find classes of witnesses that are based on half-integer powers of click moments and counts. Remarkably, this leads to an exponential increase of the number of nonclassicality criteria one can construct and apply. With this finding, special attention is payed to probing even and odd parity states, requiring such distinct witnesses. Our method is applicable to spatial and time-bin multiplexing in optical systems, where each spatial and temporal mode can be measured with both on-off detectors and detectors with partial internal quasi-photon-number resolution. Generalizations to multimode scenarios are provided, allowing for the direct measurement of nonclassical correlations and coincidence counts between an arbitrary number of modes.
The efficient certification of nonclassical effects of light forms the basis for applications in optical quantum technologies. We derive general correlation conditions for the verification of nonclassical light based on multiplexed detection. The obtained nonclassicality criteria are valid for imperfectly balanced multiplexing scenarios with on-off detectors and do not require any knowledge about the detector system. In this sense, they are fully independent of the detector system. In our experiment, we study light emitted by clusters of single-photon emitters, whose photon number may exceed the number of detection channels. Even under such conditions, our criteria certify nonclassicality with high statistical significance.
A reliable single photon source is a prerequisite for linear optical quantum computation and for secure quantum key distribution. A criterion yielding a conclusive test of the single photon character of a given source, attainable with realistic detectors, is therefore highly desirable. In the context of heralded single photon sources, such a criterion should be sensitive to the effects of higher photon number contributions, and to vacuum introduced through optical losses, which tend to degrade source performance. In this Rapid Communication we present, theoretically and experimentally, a criterion meeting the above requirements.
We consider a way to generate operational inequalities to test nonclassicality (or quantumness) of multimode bosonic fields (or multiparty bosonic systems) that unifies the derivation of many known inequalities and allows to propose new ones. The nonclassicality criteria are based on Vogel's criterion corresponding to analyzing the positivity of multimode PPP functions or, equivalently, the positivity of matrices of expectation values of, e.g., creation and annihilation operators. We analyze not only monomials but also polynomial functions of such moments, which can sometimes enable simpler derivations of physically relevant inequalities. As an example, we derive various classical inequalities which can be violated only by nonclassical fields. In particular, we show how the criteria introduced here easily reduce to the well-known inequalities describing (a) multimode quadrature squeezing and its generalizations, including sum, difference, and principal squeezing; (b) two-mode one-time photon-number correlations, including sub-Poisson photon-number correlations and effects corresponding to violations of the Cauchy-Schwarz and Muirhead inequalities; (c) two-time single-mode photon-number correlations, including photon antibunching and hyperbunching; and (d) two- and three-mode quantum entanglement. Other simple inequalities for testing nonclassicality are also proposed. We have found some general relations between the nonclassicality and entanglement criteria, in particular those resulting from the Cauchy-Schwarz inequality. It is shown that some known entanglement inequalities can be derived as nonclassicality inequalities within our formalism, while some other known entanglement inequalities can be seen as sums of more than one inequality derived from the nonclassicality criterion. This approach enables a deeper analysis of the entanglement for a given nonclassicality.