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arXiv:1302.0229 · Physical Review Letters

Direct Observation of Sub-Binomial Light

Tim J. Bartley, Gaia Donati, Xian‐Min Jin, Animesh Datta, Marco Barbieri, Ian A. Walmsley

Published Apr 25, 2013• 72 citations
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Abstract

Nonclassical states of light are necessary resources for quantum technologies such as cryptography, computation and the definition of metrological standards. Observing signatures of nonclassicality generally requires inferring either the photon number distribution or a quasiprobability distribution indirectly from a set of measurements. Here, we report an experiment in which the nonclassical character of families of quantum states is assessed by direct inspection of the outcomes from a multiplexed photon counter. This scheme does not register the actual photon number distribution; the statistics of the detector clicks alone serve as a witness of nonclassicality, as proposed by Sperling et al. [Phys. Rev. Lett. 109, 093601 (2012)]. Our work paves a way for the practical characterization of increasingly sophisticated states and detectors.

DOI
10.1103/physrevlett.110.173602

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Nonclassical states of light are necessary resources for quantum technologies such as cryptography, computation and the definition of metrological standards. Observing signatures of nonclassicality generally requires inferring either the photon number distribution or a quasiprobability distribution indirectly from a set of measurements. Here, we report an experiment in which the nonclassical character of families of quantum states is assessed by direct inspection of the outcomes from a multiplexed photon counter. This scheme does not register the actual photon number distribution; the statistics of the detector clicks alone serve as a witness of nonclassicality, as proposed by Sperling et al. [Phys. Rev. Lett. 109, 093601 (2012)]. Our work paves a way for the practical characterization of increasingly sophisticated states and detectors.
Nonclassical states of light are necessary resources for quantum technologies such as cryptography, computation and the definition of metrological standards. Distinguishing nonclassical states from those that can be described without invoking quantum mechanics is both a necessary practical task and of fundamental interest. In general, signatures of nonclassicality arise from apparently pathological behaviour of the quasi-probability distributions used to describe the states. While tomographic reconstruction of the state is therefore sufficient to show nonclassicality, it is often more convenient to probe photon-counting statistics of on-off detectors directly. This is formalised by the Mandel Q-parameter QM= 〈Δn〉 / 〈n〉 - 1, which is negative for sub-Poissonian statistics arising from nonclassical states. However, the Mandel Q-parameter can fail when using a multiplexed array of on-off detectors to measure states with several photons; splitting in this manner can corrupt its original statistics. A new parameter, QB= N 〈(Δ c) 2 〉 / 〈 c 〉 (N - 〈 c 〉) can be used to witness nonclassicality directly from such click statistics. For QB<; 0, such statistics are thus deemed sub-binomial and therefore arise from a nonclassical state.
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.
We introduce a general parameter QPB{Q}_{\mathrm{PB}}QPB​ that provides an experimentally accessible nonclassicality measure for light. The parameter is quantified by the click statistics obtained from on-off detectors in a general multiplexing detection setup. Sub-Poisson-binomial statistics, observed by QPB<0{Q}_{\mathrm{PB}}<0QPB​<0, indicates that a given state of light is nonclassical. Our parameter replaces the binomial parameter QB{Q}_{\mathrm{B}}QB​ for more general cases, where any unbalance among the multiplexed modes is allowed, thus enabling the use of arbitrary multiplexing schemes. The significance of the parameter QPB{Q}_{\mathrm{PB}}QPB​ is theoretically examined in a measurement setup that only consists of a ring resonator and a single on-off detector. The proposed setup exploits minimal experimental resources and is geared towards a fully integrated quantum nanophotonic circuit. The results show that nonclassical features remain noticeable even in the presence of significant losses, rendering our nonclassicality test more practical and sufficiently flexible to be used in various nanophotonic platforms.
Nonclassicality, defined in the quantum optical sense, serves as a resource for photon-based quantum technologies. Therefore, certifying the nonclassicality of a quantum state is crucial for gauging its potential for quantum advantage. However, traditional nonclassicality witnesses that assume perfect knowledge of the witness observables often fail in realistic scenarios with limited statistics and finite-resolution photon detectors. Furthermore, these witnesses do not exploit the fact that certain states are unlikely to be observed in a given experiment. Here, we train a variational model to distinguish classical from nonclassical states using finitely many measurement samples of multimode quantum states that are probed with different photon-number-resolving detection schemes. The learned decision rule is then an indicator of nonclassicality, tailored to a given set of physically relevant states. Our approach is both data-driven and interpretable in the sense that the learned analytical decision rule can be extracted. Training the model on experimental data measured with (i) a superconducting nanowire single-photon detector and (ii) a time-bin multiplexing detection scheme demonstrates the versatility of the approach, paving the way for efficient nonclassicality detection.
, 163602 (2017)], we introduced and applied a detector-independent method to uncover nonclassicality. Here, we extend those techniques and give more details on the performed analysis. We derive a general theory of the positive-operator-valued measure that describes multiplexing layouts with arbitrary detectors. From the resulting quantum version of a multinomial statistics, we infer nonclassicality probes based on a matrix of normally ordered moments. We discuss these criteria and apply the theory to our data which are measured with superconducting transition-edge sensors. Our experiment produces heralded multiphoton states from a parametric down-conversion light source. We show that the known notions of sub-Poisson and sub-binomial light can be deduced from our general approach, and we establish the concept of sub-multinomial light, which is shown to outperform the former two concepts of nonclassicality for our data.