Quantum algorithms offer significant speedups over their classical counterparts for a variety of problems. The strongest arguments for this advantage are borne by algorithms for quantum search, quantum phase estimation, and Hamiltonian simulation, which appear as subroutines for large families of composite quantum algorithms. A number of these quantum algorithms were recently tied together by a novel technique known as the quantum singular value transformation (QSVT), which enables one to perform a polynomial transformation of the singular values of a linear operator embedded in a unitary matrix. In the seminal GSLW'19 paper on QSVT [Gilyén, Su, Low, and Wiebe, ACM STOC 2019], many algorithms are encompassed, including amplitude amplification, methods for the quantum linear systems problem, and quantum simulation. Here, we provide a pedagogical tutorial through these developments, first illustrating how quantum signal processing may be generalized to the quantum eigenvalue transform, from which QSVT naturally emerges. Paralleling GSLW'19, we then employ QSVT to construct intuitive quantum algorithms for search, phase estimation, and Hamiltonian simulation, and also showcase algorithms for the eigenvalue threshold problem and matrix inversion. This overview illustrates how QSVT is a single framework comprising the three major quantum algorithms, thus suggesting a grand unification of quantum algorithms.

Recent theoretical and experimental studies have revealed the co-existence of heavy and light electrons in magic-angle multilayer graphene, which form a periodic lattice of Anderson impurities hybridizing with Dirac semi-metals. This work demonstrates that nontrivial features -- pairing potential, pseudogap, and continuous quantum phase transitions -- already appear at the single-impurity level, if valley-anisotropic anti-Hund's interactions ($J_S$, $J_D$) are included, favoring either a singlet ($J_S>J_D$) or a valley doublet ($J_D>J_S$) impurity configuration. We derive a complete phase diagram and analytically solve the impurity problem at several fixed points using bosonization and refermionization techniques. When $J_D>J_S,J_D>0$, the valley doublet only couples via pair-hopping processes to the conduction electrons, in sharp contrast to the conventional Kondo scenario. Upon increasing $J_D$, there is a quantum phase transition of the BKT universality class, from a Fermi liquid to an anisotropic doublet phase, the latter exhibiting power-law susceptibilities with non-universal exponents. On the other hand, when $J_S>J_D,J_S>0$, increasing $J_S$ induces a second-order phase transition from Fermi liquid to a local singlet phase, which involves a non-Fermi liquid as an intermediate fixed point. Near the transition towards the anisotropic doublet (local singlet) phase, the renormalized interaction of the Fermi liquid becomes attractive, favoring doublet (singlet) pairing. Based on analytic solutions, we construct ansatz for the impurity spectral function and correlation self-energy, which account for the pseudogap accompanying side peaks, found in recent spectroscopic measurements and a DMFT study. In particular, we obtain a non-analytic V-shaped spectral function with non-universal exponents in the anisotropic doublet phase. All results are further verified by NRG calculations.

The quantum reference frames program is based on the idea that reference frames should be treated as quantum physical systems. In this work, we combine these insights with the emphasis on operationality, understood as refraining from introducing into the framework objects not directly related to in principle verifiable probabilities of measurement outcomes, and identifying the setups indistinguishable as such. Based on intuitions from special relativity and gauge theory, we introduce an operational notion of a quantum reference frame -- which is defined as a quantum system equipped with a covariant positive operator-valued measure (POVM) -- and build a framework on the concept of operational equivalence that allows us to enforce operationality by quotienting the quantum state spaces with equivalence relation of indistinguishability by the available effects, assumed to be invariant under gauge transformations, and framed in the sense of respecting the choice of the frame's POVM. Such effects are accessed via the yen construction, which maps effects on the system to those on the composite system, satisfying gauge invariance and framing. They are called relative, and the classes of states indistinguishable by them are referred to as relative states. We show that when the frame is localizable, meaning that it allows for states that give rise to a highly localized probability distribution of the frame's observable, by restricting the relative description upon such localized frame preparation we recover the usual, non-relational formalism of quantum mechanics. We provide a consistent way of translating between different relative descriptions by means of frame-change maps and compare these with the corresponding notions in other approaches to QRF, establishing an operational agreement in the domain of common applicability.

In supergravity, charged rotating black holes are generically driven towards becoming extremal and supersymmetric through the emission of Hawking radiation. Eventually, as the black hole approaches the BPS bound and is close to becoming supersymmetric, quantum gravity corrections become critical to describing the emission of Hawking radiation, making the QFT in curved spacetime approximation inaccurate. In this paper, we compute how such quantum gravity corrections affect the spectrum of Hawking radiation for black holes in $\mathcal N=2$ supergravity in flatspace. We show that due to such corrections, the spectrum of emitted Hawking radiation for both spin-0 and spin-$1/2$ particles deviates drastically at low temperatures from the naively expected black-body spectrum. Rather remarkably, the spectrum exhibits a discrete emission line from direct transitions from near-BPS to BPS states, providing the first controlled example where the discreteness of the black hole energies is visible in the emitted Hawking radiation. Similar quantum gravity effects drastically modify the absorption cross-section: BPS black holes are transparent to certain frequencies, while near-BPS black holes appear much larger than the semi-classical prediction.

Quasars are among the most luminous sources characterized by their broad band spectra ranging from radio through optical to X-ray band, with numerous emission and absorption features. Using the Principal Component Analysis (PCA), Boroson & Green (1992) were able to show significant correlations between the measured parameters. Among the significant correlations projected, the leading component, related to Eigenvector 1 (EV1) was dominated by the anti-correlation between the Fe${\mathrm{II}}$ optical emission and [OIII] line where the EV1 alone contained 30% of the total variance. This introduced a way to define a quasar main sequence, in close analogy to the stellar main sequence in the Hertzsprung-Russel (HR) diagram (Sulentic et. al 2001). Which of the basic theoretically motivated parameters of an active nucleus (Eddington ratio, black hole mass, accretion rate, spin, and viewing angle) is the main driver behind the EV1 yet remains to be answered. We currently limit ourselves to the optical waveband, and concentrate on theoretical modelling the Fe${\mathrm{II}}$ to H$\mathrm{\beta}$ ratio, and test the hypothesis that the physical driver of EV1 is the maximum of the accretion disk temperature, reflected in the shape of the spectral energy distribution (SED). We performed computations of the H$\mathrm{\beta}$ and optical Fe${\mathrm{II}}$ for a broad range of SED peak position using CLOUDY photoionisation code. We assumed that both H$\mathrm{\beta}$ and Fe${\mathrm{II}}$ emission come from the Broad Line Region represented as a constant density cloud in a plane-parallel geometry. We compare the results for two different approaches: (1) considering a fixed bolometric luminosity for the SED; (2) considering $\mathrm{L_{bol}/L_{Edd}}$ = 1.

It is shown that the photon picture of the electromagnetic field enables one to determine unambiguously the splitting of the total angular momentum of the electromagnetic field into the orbital part and the spin part.

The black hole mass measurement in active galaxies is a challenge, particularly in sources where the reverberation method cannot be applied. We aim to determine the black hole mass in a very special object, RE J1034+396, one of the two AGN with QPO oscillations detected in X-rays, and a single bright AGN with optical band totally dominated by starlight. We fit the stellar content using the code starlight, and the broad band disk contribution to optical/UV/X-ray emission is modeled with optxagnf. We also determine the black hole mass using several other independent methods. Various methods give contradictory results. Most measurements of the blacc hole mass are in the range 1.e6-1.e7 Msun, and the measurements based on dynamics give higher values than measurements based on Hbeta and Mg II emission lines.

Recently it was shown in [New J. Phys. 8, 330 (2006)] that the three dimensional Heisenberg uncertainty principle might be signifficantly sharpened if the relevant quantum state describes the particle in a central potential. I extend that result to the case of states which are not the eigenstates of the square of the angular momentum operator. I derive a new lower bound which involves the mean value and the variance of the $\hat{L}^2$ operator.

This study is focused on the observational measurement of the viewing angle of individual quasars by modeling the broadband quasar spectrum ranging from the infra-red (IR) to the soft X-ray band. Sources are selected from various published catalogs, and their broadband quasi-simultaneous spectral data points were collected and used to model. We started with a COSMOS sample of type-1 sources which have broadband photometric points. Then, to include more data points, we cross-matched the COSMOS with the SDSS DR14 quasar catalog, and eventually, we find 90 sources that have broadband data ranging from IR to soft X-ray. The broadband spectral energy distribution (SED) modeling is done in Xspec by using the optxagnf and the SKIRTOR models for the X-ray, UV, Optical, and IR regimes for each source. The whole sample is divided into four bins with respect to redshift, black hole (BH) mass, and Eddington ratio with an equal number of sources in each bin. The viewing angle is estimated in each bin, and its evolution with respect to redshift, BH mass, and Eddington ratio is examined. As a result, we did not find any significant evolution of viewing angle with those parameters within the 95$\%$ confidence interval. We conclude that the use of quasars in cosmology to determine the expansion rate of the universe is therefore justified, and biases are not expected.

We extend our previous analysis of the motion of vortex lines [I. Bialynicki-Birula, Z. Bialynicka-Birula and C. Sliwa, Phys. Rev. A 61, 032110 (2000)] from linear to a nonlinear Schroedinger equation with harmonic forces. We also argue that under certain conditions the influence of the contact nonlinearity on the motion of vortex lines is negligible. The present analysis adds new weight to our previous conjecture that the topological features of vortex dynamics are to a large extent universal.

Here, we demonstrate that a set of coherent measurements leverages semi-device-independent (SDI) steering and local randomness generation. To this end, we show that coherent measurements are a necessary resource for demonstrating SDI steering. Conversely, through one-to-one mapping of an SDI steerable correlation to a set of measurements, the coherence of the measurements, in turn, is a necessary and sufficient criterion for SDI steering. This result aligns with the relationship between the standard steering scenario and the measurement incompatibility. Then a nonconvex resource theory for SDI steering is formulated and a nonconvex monotone of the resource is obtained in the two-setting scenario using the above-mentioned one-to-one mapping. Finally, we apply this monotone to the quantification of local randomness from two-qubit states without requiring entanglement to be certified.

Compact binary mergers and the collapse of massive stars can produce intense transients observable across high-energy wavelengths. Events such as gamma-ray bursts and kilonova emissions are often accompanied by gravitational wave detections, making them crucial sources for multimessenger astrophysics. To explore these phenomena theoretically, state-of-the-art approaches of General Relativistic magnetohydrodynamic simulations are used. We present recent findings from our simulations, and discuss observational consequences of the stellar/post-merger environment on the gamma ray burst prompt emission properties.

One of the basic observations of the classical world is that physical entities are real and can be distinguished from each other. However, within quantum theory, the idea of physical realism is not well established. A framework to analyse how observations in experiments can be described using some physical states of reality was recently developed, known as ontological models framework. Different principles when imposed on the ontological level give rise to different theories, the validity of which can be tested based on the statistics generated by these theories. Using the ontological models framework, we formulate a novel notion of classicality termed ontic-distinguishability, which is based upon the physical principles that in classical theories extremal states are physical states of reality and every sharp measurement observes the state of the system perfectly. We construct a communication task in which the success probability is bounded from above for ontological models satisfying the notion of ontic-distinguishability. Contrary to previous notions of classicality which either required systems of dimension strictly greater than two or atleast three preparations, a violation of ontic-distinguishability can be observed using just a pair of qubits and a pair of incompatible measurements. We further show that violation of previously known notions of classicality such as preparation non-contextuality and Bell's local causality is a violation of ontic-distinguishability.

We develop a new embedding-space formalism for AdS$_4$ and CFT$_3$ that is useful for evaluating Witten diagrams for operators with spin. The basic variables are Killing spinors for the bulk AdS$_4$ and conformal Killing spinors for the boundary CFT$_3$. The more conventional embedding space coordinates $X^I$ for the bulk and $P^I$ for the boundary are bilinears in these new variables. We write a simple compact form for the general bulk-boundary propagator, and, for boundary operators of spin $\ell \geq 1$, we determine its conservation properties at the unitarity bound. In our CFT$_3$ formalism, we identify an $\mathfrak{so}(5,5)$ Lie algebra of differential operators that includes the basic weight-shifting operators. These operators, together with a set of differential operators in AdS$_4$, can be used to relate Witten diagrams with spinning external legs to Witten diagrams with only scalar external legs. We provide several applications that include Compton scattering and the evaluation of an $R^4$ contact interaction in AdS$_4$. Finally, we derive bispinor formulas for the bulk-to-bulk propagators of massive spinor and vector gauge fields and evaluate a diagram with spinor exchange.

The physical origin of the Broad Line Region in Active Galactic Nuclei is still unclear despite many years of observational studies. The reason is that the region is unresolved and the reverberation mapping results imply complex velocity field. We adopt a theory-motivated approach to identify the principal mechanism responsible for this complex phenomenon. We consider the possibility that the role of dust is essential. We assume that the local radiation pressure acting on the dust in the accretion disk atmosphere launches the outflow of material, but higher above the disk the irradiation from the central parts cause the dust evaporation and a subsequent fall back. This failed radiatively accelerated dusty outflow (FRADO) is expected to represent the material forming low ionization lines. In this paper we formulate simple analytical equations describing the cloud motion, including the evaporation phase. The model is fully described just by the basic parameters: black hole mass, accretion rate, black hole spin and the viewing angle. We study how the spectral line generic profiles correspond to this dynamics. We show that the virial factor calculated from our model strongly depends on the black hole mass in case of enhanced dust opacity, and thus it then correlates with the line width. This could explain why the virial factor measured in galaxies with pseudo-bulges differs from that obtained from objects with classical bulges although the trend predicted by the current version of the model is opposite to the observed trend.

We develop a geometric approach to quantum mechanics based on the concept of the Tulczyjew triple. Our approach is genuinely infinite-dimensional and including a Lagrangian formalism in which self-adjoint (Schroedinger) operators are obtained as Lagrangian submanifolds associated with the Lagrangian. As a byproduct we obtain also results concerning coadjoint orbits of the unitary group in infinite dimension, embedding of the Hilbert projective space of pure states in the unitary group, and an approach to self-adjoint extensions of symmetric relations.

The observations of the near-infrared excess object G2/DSO induced an increased attention towards the Galactic center and its vicinity. The predicted flaring event in 2014 and the outcome of the intense monitoring of the supermassive black hole in the center of our Galaxy did not fulfill all predictions about a significantly enhanced accretion event. Subsequent observations furthermore addressed the question concerning the nature of the object because of its compact shape, especially during its periapse in 2014. Theoretical approaches have attempted to answer the contradicting behavior of the object, resisting the expected dissolution of a gaseous cloud due to tidal forces in combination with evaporation and hydrodynamical instabilities. However, assuming that the object is rather a dust-enshrouded young stellar object seems to be in line with the predictions of several groups and observations presented in numerous publications. Here we present a detailed overview and analysis of the observations of the object that have been performed with SINFONI (VLT) and provide a comprehensive approach to clarify the nature of G2/DSO. We show that the tail emission consists of two isolated and compact sources with different orbital elements for each source rather than an extended and stretched component as it appeared in previous representations of the same data. Considering our recent publications, we propose that the monitored dust-enshrouded objects are remnants of a dissolved young stellar cluster whose formation was initiated in the Circum-nuclear Disk. This indicates a shared history which agrees with our analysis of the D- and X-sources.

We present GLADE+, an extended version of the GLADE galaxy catalogue introduced in our previous paper for multimessenger searches with advanced gravitational-wave detectors. GLADE+ combines data from six separate but not independent astronomical catalogues: the GWGC, 2MPZ, 2MASS XSC, HyperLEDA, and WISExSCOSPZ galaxy catalogues, and the SDSS-DR16Q quasar catalogue. To allow corrections of CMB-frame redshifts for peculiar motions, we calculated peculiar velocities along with their standard deviations of all galaxies having $B$-band magnitude data within redshift $z=0.05$ using the "Bayesian Origin Reconstruction from Galaxies" formalism. GLADE+ is complete up to luminosity distance $d_L=47^{+4}_{-2}$ Mpc in terms of the total expected $B$-band luminosity of galaxies, and contains all of the brightest galaxies giving 90\% of the total $B$-band and $K$-band luminosity up to $d_L\simeq 130$ Mpc. We include estimations of stellar masses and individual binary neutron star merger rates for galaxies with $W1$ magnitudes. These parameters can help in ranking galaxies in a given gravitational wave localization volume in terms of their likelihood of being hosts, thereby possibly reducing the number of pointings and total integration time needed to find the electromagnetic counterpart.

We study the entangling properties of multipartite unitary gates with respect to the measure of entanglement called one-tangle. Putting special emphasis on the case of three parties, we derive an analytical expression for the entangling power of an $n$-partite gate as an explicit function of the gate, linking the entangling power of gates acting on $n$-partite Hilbert space of dimension $d_1 \ldots d_n$ to the entanglement of pure states in the Hilbert space of dimension $(d_1 \ldots d_n)^2$. Furthermore, we evaluate its mean value averaged over the unitary and orthogonal groups, analyze the maximal entangling power and relate it to the absolutely maximally entangled (AME) states of a system with $2n$ parties. Finally, we provide a detailed analysis of the entangling properties of three-qubit unitary and orthogonal gates.