Searcharxiv⌕ Search

arXiv subjects

Éva Rácz

Publications and source records attributed to Éva Rácz.

7 recordsLinked to original sources
arXiv2025

Witnessing quantum non-Gaussianity from intensity moments

Direct measurement of quantum non-Gaussianity requires some variant of a discrete photon-resolving detection, which is feasible only for low mean photon numbers. For a large mean photon number, intensity detection by linear photodiodes provides a continuous signal; therefore, the Fock probabilities of the unknown input state are not directly available. On the other hand, intensity moments can be measured directly, and photon-number moments can be estimated. Therefore, we derive and analyze a quantum non-Gaussianity witness based solely on the photon number mean and variance (or alternatively, the second-order correlation $g^{(2)}$) of an unknown state. Due to the simplicity of the used photon-number moments, the measurement results are easy to correct for losses and additive noise. We provide examples of simple amplification-based measurement schemes where our witness can be applied directly, thereby opening pathways to proof-of-principle tests and applications.

quant-ph↗
arXiv2025

Certifying non-classicality and non-Gaussianity through optical parametric amplification

Non-Gaussian states of light are essential for numerous quantum information protocols; thus, certifying non-Gaussianity is crucial. Full quantum state tomography, commonly used for this purpose, is a complicated procedure and yields inconclusive results for strongly mixed states. Certifying non-Gaussianity through directly measurable parameters is a simpler alternative, typically achieved by measuring photon-number probabilities - either directly, using photon-number resolving detectors, or through Hanbury Brown--Twiss type measurements with single-photon detectors. Here, we demonstrate theoretically and experimentally that optical parametric amplification combined with conventional intensity detectors can effectively replace this approach without the need for photon-number resolution. In our method, we measure the mean photon number and the second-order correlation function for the amplified state. Using it, we successfully certify the non-Gaussianity of a heralded quasi-single-photon state. Since optical parametric amplification is a broadband and multimode process, our method provides a foundation for developing high-dimensional quantum technologies utilizing broadband multimode non-Gaussian states.

quant-ph↗
arXiv2023

Efficient OPA tomography of non-Gaussian states of light

Current advances in nonlinear optics have made it possible to perform a homodyne-like tomography of an unknown state without highly efficient detectors or a strong local oscillator. Thereby, a new experimental direction has been opened into multimode and large-bandwidth quantum optics. An optical parametric amplifier (OPA) allows us to reconstruct the quadrature distribution of an unknown state directly from the measured intensity distribution with high precision. We propose adding a controllable displacement to the standard scheme, obtaining an improved method applicable even to asymmetric and non-Gaussian states while significantly increasing estimation accuracy and lowering the OPA amplification requirement. To demonstrate the power of our method, we accurately detect the sub-Planck phase-space structure by a distillable squeezing from the OPA estimates of various non-Gaussian states. With the improvements, OPA tomography became a generally applicable loss-tolerant and efficient alternative to OPA-assisted homodyne detection.

quant-ph↗
arXiv2020

Estimation of heavy tails in optical non-linear processes

In optical non-linear processes rogue waves can be observed, which can be mathematically described by heavy-tailed distributions. These distributions are special due to the fact that the probability of registering extremely high intensities is significantly higher than for the exponential distribution, which is most commonly observed in statistical and quantum optics. The current manuscript gives a practical overview of the generic statistics toolkit concerning heavy-tailed distributions and proposes methods to deal with issues specific to non-linear optics. We take a closer look at supercontinuum generation, where rogue waves were already observed. We propose modifications to the Hill estimator to deal with detector saturation as well as corrections introduced by pumping the process by bright squeezed vacuum. The suggested methodology facilitates statistically reliable observation of heavy-tailed distribution in non-linear optics, nanooptics, atomic, solid-state processes and optomechanics.

physics.optics↗
arXiv2011

Analytic results and weighted Monte Carlo simulations for CDO pricing

We explore the possibilities of importance sampling in the Monte Carlo pricing of a structured credit derivative referred to as Collateralized Debt Obligation (CDO). Modeling a CDO contract is challenging, since it depends on a pool of (typically about 100) assets, Monte Carlo simulations are often the only feasible approach to pricing. Variance reduction techniques are therefore of great importance. This paper presents an exact analytic solution using Laplace-transform and MC importance sampling results for an easily tractable intensity-based model of the CDO, namely the compound Poissonian. Furthermore analytic formulae are derived for the reweighting efficiency. The computational gain is appealing, nevertheless, even in this basic scheme, a phase transition can be found, rendering some parameter regimes out of reach. A model-independent transform approach is also presented for CDO pricing.

q-fin.CP↗
arXiv2009

A shift-optimized Hill-type estimator

A wide range of natural and social phenomena result in observables whose distributions can be well approximated by a power-law decay. The well-known Hill estimator of the tail exponent provides results which are in many respects superior to other estimators in case the asymptotics of the distribution is indeed a pure power-law, however,systematic errors occur if the distribution is altered by simply shifting it. We demonstrate some related problems which typically emerge when dealing with empirical data and suggest a procedure designed to extend the applicability of the Hill estimator.

physics.data-an↗