These lectures present a general critical assessment of various frameworks for quantum gravity, with particular emphasis on string theory. The topics discussed cover field-theoretical approaches to quantum gravity, anomalies, bosonic and fermionic string theories, as well as some aspects of string phenomenology and black hole physics.

We show that ultraviolet information can be extracted from low-energy expansion coefficients, assuming analyticity and the absence of massless singularities. By reorganizing the low-energy expansion through an inverse Laplace transform and a controlled coarse-graining procedure, we make ultraviolet behavior accessible beyond the cutoff of the effective field theory. In particular, we determine the sign of the beta function and the associated dynamical scale directly from the low-energy expansion of a physical observable below the mass thresholds in QED and QCD-like theories.

Micromesh Gas Structures (Micromegas) as readout of gaseous Time Projection Chambers (TPCs) are being considered in experiments investigating rare phenomena, like the nuclear double beta decay, solar axion detection and low-mass dark matter interactions, due to their good performance on spatial and energy resolution and operation stability. In addition, as they are potentially made mainly of radiopure materials like copper and kapton, they are appropriate for ultra-low background conditions. After a promising first study of the radiopurity of Micromegas readout planes, here results after dedicated development at CERN obtained from new radioassays, performed at the Canfranc Underground Laboratory combining different techniques, are presented. Activity of the isotopes in the lower parts of the 238U and 232Th natural chains has been constrained by analyzing the BiPo sequences using the BiPo-3 detector to be <0.064 and <0.016 muBq/cm2 respectively, while a lowest 40K content of 0.102+-0.030 muBq/cm2 has been determined by gamma spectroscopy using a HPGe detector; the latter value implies a reduction of a factor 34 with respect to the 40K activity quantified in the first analyzed sample. These results confirm the suitability of the use of Micromegas as extremely radiopure readouts for rare event searches.

We prove the following rigidity result: every compact three-dimensional Heterotic soliton with vanishing torsion and harmonic curvature is rigid, namely, it is an isolated point in the moduli space.

We advocate for a more stringent test problem for codes that aim to solve the equations of viscous hydrodynamics. Specifically, we discuss a nonuniform-density version of the common (uniform-density) Gaussian velocity shear test, where density gradients transverse to the direction of velocity shear cause the velocity profile to drift over time. By employing a nonunifom density, this test provides a test that the full viscous stress (and velocity shear) tensors are calculated correctly from the conserved variables, and checks the correctness of the fluxes and source terms calculated therefrom. In Appendix A, we present a detailed exposition of the Navier Stokes equations, particularly their fluxes and source terms in a variety of common coordinate systems.

This article reviews unitarization methods essential for extending Effective Field Theories (EFTs) beyond their perturbative limits, particularly in hadronic and electroweak (EW) sectors. Perturbative EFTs, like Chiral Perturbation Theory (ChPT), often violate unitarity bounds at higher energies, a breakdown observed in phenomena such as $ππ$ scattering resonances. To overcome this, non-perturbative techniques including the Inverse Amplitude Method (IAM), $K$-matrix formalism, and N/D approach are detailed. The IAM and the N/D methods resum perturbative series while preserving fundamental $S$-matrix principles: unitarity, analyticity, and causality, dynamically generating resonant behavior. The article emphasizes the unique role of dispersive frameworks, especially the Roy equations, which rigorously incorporate analyticity and crossing symmetry. It highlights their potential for future application in the electroweak sector, offering a powerful tool to constrain the Standard Model and interpret collider data.

Integrated silicon nitride (Si3N4) resonators have emerged as a leading platform for nonlinear photonics, yet generating light at wavelength in the ultraviolet (UV) has remained elusive in single-resonator systems. Here we report the first observation of fourth-harmonic generation reaching the blue and ultraviolet spectral regions in an integrated Si3N4 microring resonator. We systematically investigate the input-power dependence of the wavelength ranges supporting second-, third-, and fourth-harmonic generation, and study the input-power-dependent variation of the circulating fourth-harmonic signal in the UV. These results extend the operational bandwidth of integrated Si3N4 nonlinear photonic platforms to the lower edge of the material transparency window, enabling on-chip UV frequency conversion. Near-ultraviolet generation around 400 nm will enable on-chip excitation of defect-based quantum emitters in hexagonal boron nitride, enhance Raman spectroscopy through increased scattering cross-sections at shorter wavelengths, and support compact fluorescence-based bio-imaging platforms exploiting intrinsic cellular fluorophores.

We investigate diffusion-driven instabilities in a FitzHugh-Nagumo reaction-diffusion system with superdiffusive transport, modeled by fractional Laplacian operators with different diffusion orders for the activator and the inhibitor. A linear stability analysis yields explicit expressions for the instability threshold and the critical wavenumber and shows that superdiffusion modifies the band of unstable modes and the characteristic spatial scale of emerging patterns. We show that the threshold depends only on the ratio of the fractional exponents and on the kinetic parameters, while the spatial scale is controlled by the diffusion orders and the domain size. When the diffusion orders differ, spatial instabilities may occur even in regimes where the activator diffuses faster than the inhibitor, due to the combined effect of diffusion rates, anomalous scaling and system size. This leads to instability mechanisms that depart from the classical activator-inhibitor framework. A weakly nonlinear analysis near threshold provides the amplitude equation governing nonlinear saturation and reveals that superdiffusion promotes subcritical behavior. We also analyze the interaction between stationary and oscillatory instabilities near Turing-Hopf codimension-two points. All analytical results are supported by numerical simulations.

The existence of a new spin-zero particle with a mass below the electroweak scale is predicted by several theoretical models. Searches for resonant production of photon pairs at the LHC are able to probe these models. We present a search for a narrow resonance produced through gluon fusion that decays into a pair of photons with an invariant mass between 10 and 70 GeV, using a proton-proton collision data set from the CMS experiment. This data set, corresponding to an integrated luminosity of 54.4 fb$^{-1}$, was recorded in 2018 at a center-of-mass energy of 13 TeV using a newly introduced diphoton trigger that enabled exploration of the low-mass diphoton spectrum. No significant excess above the expected background is observed. Upper limits are set on the product of the gluon fusion production cross section and the branching fraction of the diphoton decay of a narrow resonance. An interpretation of these limits within an effective field theory framework for axion-like particles is also provided.

Emerging evidence suggests that physical systems operating as Maxwell demons, in which some subsystem of a larger system extracts heat energy from its environment in an apparent local violation of the second law, are commonplace throughout biology. Should these findings surprise us, or is Maxwell demon behavior inevitable in sufficiently large complex systems? In this Letter we pose the question of how likely it is that a random stochastic system with many degrees of freedom will operate as a Maxwell demon, considering null models for both continuous and discrete random dynamics. Our results show the probability of a finding a demon decreases at least exponentially, and in some cases double-exponentially, with the number of degrees of freedom, ultimately suggesting that large complex demons can only arise through a process of selection.

The prospect of identifying axion signals due to axion-photon coupling induced changes to the polarization has now become a reality in view of near-horizon polarimetric observations by the Event Horizon Telescope (EHT). Axion-like particles (ALPs), motivated as dark matter candidates by the strong CP problem, induce frequency-independent birefringence in linearly polarized radiation, producing observable rotations of the electric vector position angle. While previous studies have focused exclusively on axion signatures in near-horizon accretion disk emission, the relativistic jet of M87 -- extending from 10 gravitational radii to kiloparsec scales -- remains unexplored as an axion probe despite offering extended path lengths through the putative dark matter distribution. In this study, we investigate the effects of an axion cloud around the jet in M87 on the Stokes maps of relativistic jets using a stationary, axisymmetric, self-similar model for the jet and a coherent, homogeneous soliton core in M87's galactic center for the axion background. At 230 GHz, for representative couplings in range $g_{a γ} \sim 5 \times 10^{-15} - 5 \times 10^{-14} GeV^{-1}$, we find that axion masses in the $10^{-21} eV $ range produce degree-level to multi-degree EVPA rotations, in some cases exceeding typical EHT measurement uncertainties, whereas masses in the $10^{-22} eV$ range yield predominantly sub-degree rotations. We identify a suite of morphological diagnostics that together constitute a framework for distinguishing axion-induced birefringence from plasma Faraday rotation in resolved jet polarimetry.

We study electron transport in a strained graphene sheet subjected to a sequence of $N$ electrostatic and magnetic barriers. Employing a modified and improved transfer-matrix framework, we examine how the transmission and reflection coefficients evolve with variations in uniaxial strain and in the number of barriers. The interplay of mechanical deformation and external magnetic fields is found to generate an anomalous Klein tunnelling, allowing the conductance to be effectively modulated through strain and barrier configurations. These findings highlight the role of strain engineering and magnetic field modulation as powerful tools for tailoring charge transport in two-dimensional materials. More broadly, they underscore how mechanical and electromagnetic control can be used to design next-generation solid-state devices with tunable electronic properties.

We investigate geometric regularization strategies for learned latent representations in encoder--decoder reduced-order models. In a fixed experimental setting for the advection--diffusion--reaction (ADR) equation, we model latent dynamics using a neural ODE and evaluate four regularization approaches applied during autoencoder pre-training: (a) near-isometry regularization of the decoder Jacobian, (b) a stochastic decoder gain penalty based on random directional gains, (c) a second-order directional curvature penalty, and (d) Stiefel projection of the first decoder layer. Across multiple seeds, we find that (a)--(c) often produce latent representations that make subsequent latent-dynamics training with a frozen autoencoder more difficult, especially for long-horizon rollouts, even when they improve local decoder smoothness or related sensitivity proxies. In contrast, (d) consistently improves conditioning-related diagnostics of the learned latent dynamics and tends to yield better rollout performance. We discuss the hypothesis that, in this setting, the downstream impact of latent-geometry mismatch outweighs the benefits of improved decoder smoothness.

Inspired by recent experiments of cells accumulating on anisotropic substrates, we study a two-dimensional, compressible, isotropic, active fluid in the presence of anisotropic friction. We find that regions of anisotropic friction that are patterned as positive topological defects may drive accumulation of an active fluid into a clump, but the robustness of this behavior depends on the initial configuration. If the initial azimuthal symmetry is sufficiently broken, we find that patterning asymmetry can instead lead to circular motion of accumulated clumps. We develop an approximate analytical model to qualitatively explain the motion. Finally, we use our simplified model to design a substrate pattern that creates directed motion of accumulated clusters along a given path.

Multiparty quantum key agreement (MQKA) enables $n \geq 3$ mutually distrustful users to establish a shared secret key through collaborative quantum protocols. In this paper, we provide a comprehensive review where we argue that MQKA is best understood as a design space organized along three orthogonal but tightly coupled axes: (1) network architecture, which determines how quantum states flow between participants; (2) quantum resources, which encode the physical degrees of freedom used for implementation; and (3) security model, which defines trust assumptions about devices and infrastructure. Rather than treating MQKA as a linear sequence of isolated protocols, we develop this three-axis perspective to reveal recurrent patterns, sharp trade-offs, and unexplored design spaces. We classify MQKA protocols into structural families, map them to underlying quantum resources, and analyze how different security models shape fairness and collusion resistance. We further identify open challenges in composable security frameworks, network native integration, device-independent implementations, and propose a research roadmap toward hybrid-resource, bosonic-code-encoded, and fairness-aware MQKA suitable for the future quantum internet deployments in the post-NISQ era.

Machine learning interatomic potentials (MLIPs) evaluate potential energy surfaces orders of magnitude faster while maintaining accuracy comparable to first-principles calculations, and universal MLIPs that cover most of the periodic table are becoming increasingly commonplace. However, existing large-scale datasets have limited or no coverage of heavy elements such as minor actinides crucial in the nuclear field, and universal MLIPs are typically limited to 89 elements. Here, we constructed a heavy element dataset HE26 containing minor actinides, based on experimental and computational literature data. By integrating this with existing molecular and crystal datasets, we developed an open-source universal MLIP covering 97 elements, the broadest elemental coverage to date. The resulting model showed strong performance on the inorganic MPtrj and organic OFF23 test sets and promising accuracy on HE26. The dataset and model open a pathway toward the development of energy resources and the design of novel materials, such as actinide-based high-entropy ceramics, in the nuclear field.

A recent notion of geodesic flows which comes out of noncommutative geometry but which is also novel in the classical case is studied in detail for a Schwarzschild spacetime. In this framework, the geodesic velocity field is an independent concept which then defines the flow of a density $ρ$ on spacetime or possibly that of an amplitude wave function $ψ$ with $ρ= |ψ|^2$. The proper time flow parameter $s$ is generated collectively by the flow of matter. We show carefully how the $ρ$ evolution can be justified as modelling a large number of geodesics interpolated as a local density. Using Kruskal-Szekeres coordinates, we show that there are no issues crossing the horizon. A novel feature is that whereas two colliding Gaussian bumps in density $ρ$ merge into a single bump, two colliding wave function $ψ$ bumps of opposite phase merge into a dipole with a different density $|ψ|^2$ profile, providing a potential test of our wave-function hypothesis. We also revisit the Klein-Gordon flow or pseudo-quantum mechanics around a black-hole and find that previously found black-hole atom states and modes generated at the horizon when an area of disturbance approaches it are also present inside the black-hole in a reflected fashion. We argue that the behaviour of the horizon modes across the horizon as well as discretisation of the atomic spectrum depend on quantum gravity corrections at the horizon.

The recent discovery of unconventional momentum-dependent magnetic orders has expanded the landscape of magnetism beyond conventional ferromagnetism and antiferromagnetism. Among them, $p$-wave magnets ($p$WMs) represent a novel class of odd-parity, non-collinear compensated magnetic order that generates spin-split electronic bands. In this work, our theoretical investigation establishes $p$WMs as a versatile platform for realizing intriguing superconducting phases including topological superconductivity (TSC), Bogoliubov Fermi surfaces (BFSs), and superconducting diode effect (SDE), within a unified microscopic framework. Employing a minimal model incorporating $p$-wave magnetic order, exchange coupling, and Zeeman fields, we perform a self-consistent mean-field analysis and uncover a rich phase diagram featuring unconventional finite-momentum Fulde-Ferrell (FF) and Larkin-Ovchinnikov (LO) superconducting phases. Remarkably, we also show that $p$WMs can undergo a transition to a TSC phase anchoring Majorana flat edge modes, a hallmark of two-dimensional TSCs, even without Rashba spin-orbit coupling and Zeeman field. Upon applying a Zeeman field, gapless FF and LO phases emerge with BFSs characterized by the appearance of finite zero-energy quasiparticle density of states. Furthermore, we demonstrate that SDE arises naturally in the asymmetric FF phase. Our analysis manifests that $p$WMs serve as a unique and novel platform to host TSC phase, gapless superconducting states, and non-reciprocal transport phenomena.

Detector dead time is typically treated as a fixed parameter in quantum key distribution (QKD) security analyses. In practice, however, the effective recovery time of single-photon avalanche photodiodes (SPADs) depends on the incident count rate. In this work, we demonstrate that this count-rate-dependent recovery nonlinearity constitutes a distinct attack primitive. We experimentally characterize the dead time shift of a free-running SPAD under controlled broadband loading and observe a substantial increase in effective recovery time as the detected rate rises into the high photon count regime. We show that recovery-induced availability reduction can be modeled as an adversarial erasure channel and derive a conservative bound on the signal detection probability under loading. Unlike previously studied detector-control or efficiency mismatch attacks, the proposed mechanism does not rely on deterministic blinding or timing discrimination. Instead, count-rate-dependent recovery asymmetry induces basis-dependent suppression of detection probabilities ($p_\perp<p_\parallel$), converting mismatch-induced errors into loss. Particularly, we show in active-basis BBM92 systems, this effect reduces the observed quantum bit error rate (QBER) below the abort threshold while increasing erasure probability. Using experimentally measured detector recovery data, we quantify the parameter regime in which such stealth suppression is achievable. These results establish count-rate-dependent detector recovery as a security-relevant vulnerability and show that countermeasures designed for timing-based efficiency mismatch do not directly address recovery-induced erasure (RIE) attack. Our findings underscore the need to incorporate detector recovery dynamics explicitly into practical QKD security models.

We present 225 and 350 GHz imaging of the iconic T Tauri system using the Atacama Large Millimeter submillimeter Array (ALMA). T Tauri is a hierarchical triple system, and the close binary T Tau Sa/Sb underwent periastron passage in March 2023. The ALMA images were obtained in epochs spanning November 2019 through June 2023, and therefore covered the time frame of the recent periastron passage. We clearly resolve the Sa-Sb binary in two epochs of high-resolution measurements with ALMA. We find increases in millimeter flux from heating of the Sa disk and the wider distribution of dust in the environment of the binary. This heating is likely in response to increased stellar accretion activity triggered by orbital motion during the dynamic periastron passage of T Tau Sb around Sa. Resolved, extended millimeter emission is also found to change morphology and increase in flux in the immediate environment of the Sa-Sb binary after periastron passage. This may suggest an increase in nonthermal emission from magnetic interaction, gravitational disruption of the circumstellar disks as the stars passed through periastron, or both of these phenomena. We also detected structures in the compact (24 au radius), thermal dust disk around T Tau N. In particular, we identify a crescent-shaped emission excess just outside a shallow gap at 12 au radius that appears to move at Keplerian speed. Future measurement of dust spectral indices can clarify the origin of increased and variable millimeter emission in the environment of the T Tau S binary.

In standard multi-field models, tachyonic isocurvature perturbations generally indicate the presence of an instability. We revisit the stability of some known counterexamples and show that, in a certain class of models that we call ultra slow-turn, an exponentially decreasing turn rate can shut off this potential instability. We argue that the stability of a given model can be correctly inferred by the total entropy perturbation, even if the effective mass squared of the isocurvature perturbation is negative. Several recent supergravity- or string-inspired models such as fibre inflation, SL(2,$\mathbb{Z}$) attractors and modular inflation fall into the ultra slow-turn class.

We study quasinormal modes of scalar, electromagnetic, and Dirac perturbations of four-dimensional regular black holes arising in non-polynomial quasi-topological gravity. Starting from a more general class of metric functions constructed within the same framework, from which two representative cases are selected for detailed analysis, we examine their spectral properties. While the fundamental mode changes smoothly with the regularization parameter, higher overtones display a markedly enhanced sensitivity to near-horizon modifications, leading to the characteristic outburst of overtones. Remarkably, pushing the WKB approximation to sufficiently high orders with Pade resummation already allows one to detect the onset of this effect. Time-domain analysis and the Leaver method confirm that the relative error of the higher-order WKB approach is much smaller than the observed effect. Our results indicate that overtone dynamics provides a sensitive probe of geometrically regular black holes and that high-order WKB methods remain capable of capturing nontrivial spectral features beyond the fundamental mode.

Semiconductor quantum dots host a rich manifold of excitonic complexes, including neutral excitons that emit anti-bunched single photons and charged exciton complexes capable of producing super-bunched photons via cascade emission. Accessing both emission regimes from a single emitter would open routes to novel quantum protocols, including advanced quantum imaging. In practice, however, emission from charged exciton complexes is intrinsically weak, often orders of magnitude dimmer than neutral excitons, placing simultaneous dual-mode operation out of reach. Here, we overcome this limitation by embedding the quantum dot in a dielectric Mie-resonant metasurface that provides order-of-magnitude photoluminescence enhancement across both neutral and charged exciton transitions of a single GaAs quantum dot. Under identical non-resonant pumping conditions, the emission from the neutral exciton yields anti-bunched emission ($g^{(2)}(0) < 0.5$) and the emission from positively charged exciton complexes shows super-bunched emission ($g^{(2)}(0) > 3.5$) with comparable count rates (~12 kHz). Crucially, super-bunching emerges only when charged exciton emission spectrally overlaps with the Mie resonances and vanishes in un-patterned slabs, demonstrating that photonic engineering, is essential for accessing these weak quantum light states. These results demonstrate a scalable, position-tolerant platform for harnessing the full excitonic structure of solid-state emitters.

Quantum non-Gaussian states and operations serve as fundamental resources for universal quantum computation, error correction, and high-precision metrology, extending beyond the Gaussian limits. While the stellar rank provides a rigorous hierarchical measure of non-Gaussianity, it remains challenging to determine experimentally. Conversely, witnesses of non-Gaussian features, based on the expectation values and variances of measurable observables, offer an accessible method for certifying non-Gaussian behavior but lack a direct connection to stellar rank. In this work, we establish a quantitative connection between these witnesses and stellar rank, demonstrating that the former can provide certifiable lower bounds on stellar rank. We introduce normalized expectation value and variance-based quantifiers and show that these witnesses form a consistent hierarchy of thresholds corresponding to stellar rank. Our results bridge the gap between abstract hierarchical measures and experimentally accessible quantifiers, enabling scalable certification of non-Gaussian states.

We derive exact, convergent representations of multiloop sunset Feynman integrals in two dimensions for arbitrary mass configurations and all loop orders valid for large Euclidean momentum. The integrals are expressed as sums of symmetric polynomials in logarithmic mass ratios, normalized by the external momentum squared, with coefficients determined by analytic series expansions. For the equal-mass case, we establish a dimension-raising relation expressing the $L$ loop sunset integrals in $D+2$ as the one in $D$ dimensions acted on a differential operator of order $L-1$. These representations are free of complicated transcendental functions, making them well-suited to both formal analysis and high-precision numerical evaluation. The two-dimensional results serve as boundary conditions for dimension-shifting relations, enabling systematic reconstruction of four-dimensional sunset integrals via analytic continuation to $D = 4 - 2ε$.

We show how entanglement-assisted codes can be constructed from arbitrary quantum codes by associating them with quantum codes for erasure channels. If a subset of physical qubits is correctable for an erasure error, then it naturally forms the receiver's share of a bipartite state that can be used for entanglement-assisted communications, both in the noiseless and noisy ebit error models. In the case of degenerate codes, we show that the receiver's share of the bipartite state can sometimes be compressed, at the cost of potentially reduced error-correction ability in the noisy ebit error model. We also give examples of permutation-invariant and XP-stabilizer entanglement-assisted codes, the first outside of the stabilizer and codeword-stabilized frameworks.

Mesozooplankton aggregations undergoing vertical migrations in the upper ocean have been hypothesized to have an important role in the redistribution of carbon, nutrients, and oxygen via biogenic hydrodynamic transport (BHT). While laboratory studies have demonstrated how swarm-induced hydrodynamic instabilities can drive large-scale transport in strongly stratified environments, measurements are usually performed with model organisms that differ in morphology and swimming mode from ecologically relevant marine species. To bridge this gap, we conducted experiments with copepods and analyzed upward and downward trajectories to identify differences in flow fields, force distribution, and BHT for these two scenarios. Using two-dimensional bright-field Particle Image Velocimetry (PIV), we quantified the near-body velocity field and found that the average downward swimming speed significantly exceeds the average upward swimming speed, with the flow fields exhibiting direction-dependent characteristics. We incorporated these findings into a continuum squirmer model to estimate the swimmer-induced drift volume and mixing efficiency, focusing on the effects of the reduced gravity of the swimmers and the density stratification of the surrounding fluid. Our simulations reveal that both the excess weight of the organisms and the fluid stratification strongly constrain the net BHT. This study provides a critical step toward integrating lab-based models of marine mesozooplankton with remote sensing data to incorporate vertical migrations into global ocean models with realistic biogeochemistry and assess their ecological significance in actively sustaining local ecosystems.

We numerically evaluate the two-loop QCD squared matrix element for in $q\bar{q}\to Z$ and $q\bar{q}\to Zγ$ with heavy top and bottom quarks circulating in a triangular fermion loop, by simultaneously subtracting infrared, ultraviolet, and threshold singularities directly in loop momentum space. This computation serves as an explicit demonstration that axial couplings can be included in the final state within the framework of arXiv:2510.18801. By formulating the entire calculation in four spacetime dimensions, with anomaly cancellation realised locally in loop momentum space, we bypass the complications associated with treating $γ^5$ in dimensional regularisation.

We numerically compute the two-loop QCD corrections to $Zγ$ production at the LHC mediated by light- and heavy-quark box loops. The calculation employs the pipeline of refs. arXiv:2407.18051 and arXiv:2510.18801, which performs Monte Carlo integration over spatial loop momenta after local subtraction of infrared, ultraviolet, and threshold singularities. We validate our results for partonic squared matrix elements with massless-quark loops against known benchmarks, extend them to include heavy-quark contributions, and compute the double-virtual corrections to $pp\to Zγ$ by performing the loop and phase space integrations simultaneously. This computation demonstrates the flexibility of the approach in handling both massless and massive final-state bosons, as well as additional mass scales in the loop.

Experimental data in particle and nuclear physics, particle astrophysics, and radiation protection dosimetry are collected using experimental facilities that consist of a complex system of sensors, electronics, and software. Measured spectra or cross sections are considered as Probability Density Functions (PDFs) that deviate from true PDFs due to resolution, bias, and efficiency effects. Unfolding is viewed as a procedure for estimating an unknown true PDF. Reliable estimates of the true PDF are necessary for testing theoretical models, comparing results from different experiments, and combining results from various research endeavors. Both external and internal quality assessment methods can be applied for this purpose. In some cases, external criteria exist to evaluate deconvolution quality. A typical example is the deconvolution of a blurred image, where the sharpness of the restored image serves as an indicator of quality. However, defining such external criteria can be challenging, particularly when a measurement has not been performed previously. This paper discusses various internal criteria for assessing the quality of the results independently of external information, as well as factors that influence the quality of the unfolded distribution.