Nonclassicality Criteria Research Articles

Normal Order Non-Classical Criteria In Non-Degenerate Four-Wave Mixing Process: Quantum Entanglement, Squeezing And Anti-Bunching

Normal Order Non-Classical Criteria In Non-Degenerate Four-Wave Mixing Process: Quantum Entanglement, Squeezing And Anti-Bunching

Tight nonclassicality criteria for unbalanced Hanbury Brown–Twiss measurement scheme with click detectors

Tight nonclassicality criteria for unbalanced Hanbury Brown–Twiss measurement scheme with click detectors

Transforming photon statistics through zero-photon subtraction

Zero-photon subtraction (ZPS) is a conditional measurement process that can reduce the mean photon number of quantum optical states without physically removing any photons. Here we show that ZPS can also be used to transform certain super-Poissonian states into sub-Poissonian states and vice versa. Combined with a well-known ``no-go'' theorem on conditional measurements, this effect leads to a set of nonclassicality criteria that can be experimentally tested through ZPS measurements.

Nonclassicality detection from few Fock-state probabilities

Experimentally certifying the nonclassicality of quantum states in a reliable and efficient way is a challenge that remains both fundamental and daunting. Despite decades of topical research, techniques that can exploit optimally the information available in a given experimental setup are lacking. Here, we introduce a different paradigm to tackle these challenges, that is both directly applicable to experimental realities, and extendible to a wide variety of circumstances. We demonstrate that Klyshko’s criteria, which remained a primary approach to tackle nonclassicality for the past 20 years, is a special case of a much more general class of nonclassicality criteria. We provide both analytical results and numerical evidence for the optimality of our approach in several different scenarios of interest for trapped-ion, superconducting circuits, optical and optomechanical experiments with photon-number resolving detectors. This work represents a significant milestone towards a complete characterisation of the nonclassicality detectable from the limited knowledge scenarios faced in experimental implementations.

Measuring higher-order photon correlations of faint quantum light: A short review

Normalized correlation functions provide expedient means for determining the photon-number properties of light. These higher-order moments, also called the normalized factorial moments of photon number, can be utilized both in the fast state classification and in-depth state characterization. Further, non-classicality criteria have been derived based on their properties. Luckily, the measurement of the normalized higher-order moments is often loss-independent making their observation with lossy optical setups and imperfect detectors experimentally appealing. The normalized higher-order moments can for example be extracted from the photon-number distribution measured with a true photon-number-resolving detector or accessed directly via manifold coincidence counting in the spirit of the Hanbury Brown and Twiss experiment. Alternatively, they can be inferred via homodyne detection. Here, we provide an overview of different kind of state classification and characterization tasks that take use of normalized higher-order moments and consider different aspects in measuring them with free-traveling light.

Nonclassicality criteria for N -dimensional optical fields detected by quadratic detectors

Non-classicality criteria for general N-dimensional optical fields are derived. They involve intensity moments, the probabilities of photon-number distributions or combinations of both. The Hillery criteria for the sums of the probabilities of even or odd photon numbers are generalized to N-dimensional fields. As an example, the derived non-classicality criteria are applied to an experimental 3-mode optical field containing two types of photon-pair contributions. The accompanying non-classicality depths are used to mutually compare their performance.

Two-beam light with ’checkered-pattern’ photon-number distributions

Photon-number-resolved post-selection on one beam out of a correlated system of three beams with bi-partite photon-number correlations gives rise to joint photon-number distributions with the probabilities forming checkered patterns. These patterns originate in the convolution of two constituting photon-number distributions, one endowed with correlations in photon numbers, the other exhibiting anti-correlations in photon-number fluctuations. Using three twin beams of comparable intensity whose constituting beams suitably overlap on the photocathode of a photon-number-resolving iCCD camera, we experimentally as well as theoretically analyze the properties of such states as they change with the varying ratio of the correlated and anti-correlated contributions. The experimental photocount 2D histograms of the fields post-selected by the iCCD camera that are reconstructed by the maximum-likelihood approach confirm their non-classicality though the limited detection efficiency in post-selection conceals the checkered patterns. Contrary to this, the maximum-likelihood reconstruction of the experimental 3D photocount histogram similarly as a suitable 3D Gaussian fit, that reveal the states as they would be obtained by ideal post-selection, provide the photon-number distributions with the checkered patterns. The corresponding quasi-distributions of integrated intensities are determined. Nonclassical properties of the generated states are investigated using suitable non-classicality criteria and the corresponding non-classicality depths. These states with their correlations of varying intensity are prospective for two-photon excitations of atoms and molecules as well as two-photon spectroscopy.

Two-beam light with simultaneous anticorrelations in photon-number fluctuations and sub-Poissonian statistics

Two twin beams with a shared signal beam and separated idler beams are used together with the photon-number-resolving postselection in the signal beam to arrive at two coupled beams with anticorrelations in photon-number fluctuations. Moreover, the beams exhibit the sub-Poissonian photon-number statistics in their marginal distributions under suitable conditions. The postselected fields with the increasing mean photon numbers are reconstructed from the experimental photocount histograms by the maximum likelihood approach. Also a suitable Gaussian fit of both original twin beams and simulation of the postselection process are applied to arrive at the corresponding photon-number distributions. Their nonclassical properties are analyzed by suitable nonclassicality criteria and quantified by the corresponding nonclassicality depths. Determining the appropriate quasi-distributions of integrated intensities with negative values, the performance of different nonclassicality criteria is judged. Properties of the postselected fields reached both by the used and ideal photon-number-resolved detectors are mutually compared.

Phase squeezing of quantum hypergraph states

Corresponding to a hypergraph G with d vertices, a quantum hypergraph state is defined by , where f is a d-variable Boolean function depending on the hypergraph G, and denotes a binary vector of length 2 d with 1 at the nth position for n = 0, 1, …(2 d − 1). The nonclassical properties of these states are studied. We consider the annihilation and creation operator on the Hilbert space of dimension 2 d acting on the number states . The Hermitian number and phase operators, in finite dimensions, are constructed. The number-phase uncertainty for these states leads to the idea of phase squeezing. We establish that these states are squeezed in the phase quadrature only and satisfy the Agarwal–Tara criterion for nonclassicality, which only depends on the number of vertices of the hypergraphs. We also point out that coherence is observed in the phase quadrature.

Nonclassicality and entanglement criteria for bipartite optical fields characterized by quadratic detectors. II. Criteria based on probabilities

Numerous non-classicality criteria based on the probabilities of experimental photocount or theoretical photon-number distributions are derived using several approaches. Relations among the derived criteria are revealed and the fundamental criteria are identified. They are grouped into parametric systems that allow the analysis of the non-classicality from different points of view ('local' non-classicality, pairwise character of photon correlations, etc.). Considering their structure, the criteria may be divided into groups that differ in the power to resolve the non-classicality. Quantification of the non-classicality using the Lee non-classicality depth and the non-classicality counting parameter is discussed. The used number of field's modes is identified as an important parameter that may cause unexpected results. An appropriate linear transformation of a photocount (photon-number) distribution into its s-ordered form, needed for the determination of the non-classicality depth, is derived. For comparison, the derived criteria are applied both to an experimental photocount histogram of a twin beam and the reconstructed photon-number distributions with different levels of the noise.

Probing nonclassicality with matrices of phase-space distributions

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.

Non-classicality of optical fields as observed in photocount and photon-number distributions.

Non-classicality criteria for optical fields based on the probabilities of photocount and photon-number distributions are derived. Relations among the criteria obtained by the applied methods are revealed. Redundant criteria are identified. The performance of the fundamental criteria is tested on a set of potentially sub-Poissonian fields generated by photon-number-resolved post-selection from a mesoscopic twin beam. The corresponding non-classicality depths are determined to quantitatively compare the used criteria.

Dermoscopic Findings in the Presurgical Evaluation of Basal Cell Carcinoma. A Prospective Study.

Surgery is the best treatment for basal cell carcinoma (BCC); however, incomplete excisions are possible. Assessment of the accurateness of dermoscopy and clinical evaluation in the detection of borders of BCC and description of dermoscopic findings in clinically healthy tissue surrounding BCC. Eighty-eight lesions with clinical dermoscopic diagnosis of BCC were examined clinically and dermoscopically, to delineate the correct site of surgical incision, demarcating the respective margins with colred dermographic pencils. Specific dermoscopic features were searched in the skin adjacent to the demarcated clinical margin. In 29 of 88 lesions, clinical and dermoscopic margins of the tumor coincided. In the remaining 59 (67%), 10 (16.9%) presented, in the lesion area identified under dermoscopy, classical criteria for BCC and 57 (96.6%) nonclassical criteria. Differences between clinical and dermoscopic margins were significantly more frequent in superficial BCCs (p = .006). The frequency was not significantly different (p = .85) in relation to body sites. Dermoscopy improves the identification of margins for surgical excision in BCC. The observation of nontraditional dermoscopic criteria of BCC, mainly pink-white areas and short telangiectasias in the area between clinically and dermoscopically detected margins, helps to define the actual tumoral margins and to achieve a really radical excision.

Experimental Quantification of the Entanglement of Noisy Twin Beams

Gradual loss of the entanglement of a twin beam containing around 25 photon pairs with the increasing external noise is experimentally investigated. The entanglement is quantified by the non-classicality depths and the non-classicality counting parameters related to several non-classicality criteria. The reduction of intensity moments of the analyzed multi-mode twin beams to single-mode ones allows to determine the negativity as another quantifier of the entanglement. Both the raw photocount histograms and the reconstructed photon-number distributions are analyzed in parallel.

Detection-device-independent verification of nonclassical light

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.

Entropic nonclassicality and quantum non-Gaussianity tests via beam splitting

We propose entropic nonclassicality criteria for quantum states of light that can be readily tested using homodyne detection with beam splitting operation. Our method draws on the fact that the entropy of quadrature distributions for a classical state is non-increasing under an arbitrary loss channel. We show that our test is strictly stronger than the variance-based squeezing condition and that it can also be extended to detect quantum non-Gaussianity in conjunction with phase randomization. Furthermore, we address how our criteria can be used to identify single-mode resource states to generate two-mode states demonstrating EPR paradox, i.e., quantum steering, via beam-splitter setting.

Impact of photon addition and subtraction on nonclassical and phase properties of a displaced Fock state

Various nonclassical and quantum phase properties of photon added then subtracted displaced Fock state have been examined systematically and rigorously. Higher-order moments of the relevant bosonic operators are computed to test the nonclassicality of the state of interest, which reduces to various quantum states (having applications in quantum optics, metrology and information processing) in different limits ranging from the coherent (classical) state to the Fock (most nonclassical) states. The nonclassical features are discussed using Klyshko’s, Vogel’s, and Agarwal–Tara’s criteria as well as the criteria of lower- and higher-order antibunching, sub-Poissonian photon statistics and squeezing. In addition, phase distribution function and quantum phase fluctuation have been studied. These properties are examined for various combinations of number of photon addition and/or subtraction and Fock parameter. The examination has revealed that photon addition generally improves nonclassicality, and this advantage enhances for the large (small) values of displacement parameter using photon subtraction (Fock parameter). The higher-order sub-Poissonian photon statistics is only observed for the odd orders. In general, higher-order nonclassicality criteria are found to detect nonclassicality even in the cases when corresponding lower-order criteria failed to do so. Photon subtraction is observed to induce squeezing, but only large number of photon addition can be used to probe squeezing for large values of displacement parameter. Further, photon subtraction is found to alter the phase properties more than photon addition, while Fock parameter has an opposite effect of the photon addition/subtraction. Finally, nonclassicality and non-Gaussianity is also established using Q function.

Criteria for single photon sources with variable nonclassicality threshold

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.

Thermal-difference states of light: true states of heralded photons

We introduce a three-parameter family of single-mode optical states whose density operator is a weighted difference of two thermal states, the thermal-difference states. We identify the parameter values for which these states have a negative non-singular P-function, implying they are nonclassical. We show that the states of the “heralded photons” generated via spontaneous parametric downconversion belong to this family, with the three parameters corresponding to the nonlinear gain and the losses in the signal and the idler channels. The thermal-difference states yield new benchmark states for the analysis of nonclassicality and quantum macroscopicity criteria.

Probing Nonclassicality of Two-Mode SU(2) Generator Based on Quantum Fisher Information* *Supported by the National Natural Science Foundation of China under Grant No. 11365006 and the Natural Science Foundation of Guizhou Province under Grant No. QKHLHZ[2015]7767

Nonclassicality is an essential but still open question in quantum mechanics. Here, utilizing the maximum value of quantum Fisher information, we suggest a new version of the nonclassical criterion for SU(2) generator realized by two bosonic modes. As an application of the criterion, the system of two coupled nonlinear nanomechanical resonators is considered. And the nonclassicality of the phonon state in the dynamical evolution is explored. The system has a dynamical phase transition from the tunnelling phase to the self-trapping phase by tuning the coupling strength. It is found that for the tunnelling phase, the phonon state is nonclassical in the full time evolution. And for the self-trapping phase, the evolved phonon state is still nonclassical in the full time with a relatively large coupling strength, while it is nonclassical i n the most of time (but not all) with a small coupling strength. Quantum coherence has distinct different behaviors in the two phases.