We find the quasi-inverse of qubit channels as a unitary map ${\mathcal{E}}^i$ by minimizing the average trace distance between the input state to the channel and the output of the quasi-inverse channel for an arbitrary qubit channel $\mathcal{E}$ and for arbitrary input states. The channel $\mathcal{E}$ is assumed to be completely positive and trace preserving. To find the quasi-inverse for mixed states, we propose an alternative definition of the quasi-inverse based on the mean-square trace distance (MSTD) of a channel. The definition based on the trace distance allows easy generalization of the quasi-inverse to mixed input states. The quasi-inverse of the Pauli, generalized amplitude damping, mixed unitary, and tetrahedron channels calculated based on the MSTD agrees with the one computed using average fidelity in the special case of input states being pure.

Quantum process tomography (QPT) is crucial for advancing quantum technologies, including quantum computers, quantum networks, and quantum sensors. Shadow process tomography (SPT) utilizes the Choi isomorphism to map QPT to shadow state tomography (SST), significantly reducing the sample complexity for extracting information from quantum processes. However, SPT relies on random unitary operators and complicates the determination of the optimal unitary operator that minimizes the shadow norm, which is the key factor influencing the sample complexity. In this work, we propose a generalized SPT framework that minimizes the shadow norm by replacing unitary operators with generalized measurements [positive operator-valued measures (POVMs)]. This approach, termed shadow process tomography with POVMs (POVM-SPT), uses convex optimization to identify the optimal POVM for minimizing the shadow norm, thereby further reducing sample complexity. We demonstrate the identification of the optimal POVM through numerical simulations and provide the corresponding optimization algorithms. Our numerical experiments demonstrate that POVM-SPT achieves a substantial reduction in the shadow norm compared to conventional SPT, with an approximate sevenfold improvement for single-qubit input states and a remarkable $2^{180}$-fold enhancement for 64-qubit input states. These results reveal that POVM-SPT offers significant advantages in simplifying SPT tasks, particularly for large-scale quantum systems.

D-Wave quantum annealers offer reverse annealing as a feature allowing them to refine solutions to optimization problems. This paper investigates the influence of key parameters, such as annealing times and reversal distance, on the behavior of reverse annealing by studying models containing up to 1000 qubits. Through the analysis of theoretical models and experimental data, we explore the interplay between quantum and classical processes in describing the empirical data. Our findings provide a deeper understanding that can better equip users to fully harness the potential of the D-Wave annealers.

Quantum key distribution requires tight and reliable bounds on the secret key rate to ensure robust security. This is particularly so for the regime of finite block sizes, where the optimization of generalized Rényi entropic quantities is known to provide tighter bounds on the key rate. However, such an optimization is often nontrivial. In this work, we present an analytical bound on the Rényi entropy in terms of the Rényi divergence and derive the analytical gradient of the Rényi divergence. This enables us to generalize existing state-of-the-art numerical frameworks for the optimization of key rates. With this generalized framework, we show improvements in regimes of high loss and low block sizes, which are particularly relevant for long-distance satellite-based protocols.

We report measurements of the $D_1$ and $D_2$ transition energies in Na-like Ir (${\mathrm{Ir}}^{66+}$). The $D_{1}3s\text{−}3p_{1/2}$ transition energy, measured in the extreme ultraviolet (EUV) region at $169.977\pm 0.005$ eV with a relative uncertainty of 29 ppm, represents one of the most precise $D$-line energy measurements to date for high atomic numbers $Z\ge 30$. The $D_{2}3s\text{−}3p_{3/2}$ transition energy, measured in the x-ray region, is $621.11\pm 0.06$ eV. Therefore, there is a fine-structure separation of $451.13\pm 0.06$ eV for the Na-like Ir $3p$ levels. We present theoretical calculations of these energies using quantum electrodynamic-extended relativistic many-body perturbation theory and multiple-configuration Dirac-Hartree-Fock methods, and discuss the discrepancies between experimental and theoretical values. The prospect of determining the absolute nuclear charge radii of heavy elements, including rare isotopes, from these measurements is explored.

We investigate the spin states obtained by extracting $n$ electrons from closed-shell fermionic states. A partition of the system is defined through the introduction of the extraction modes. We derive the expression of the $n$-body reduced density matrices, which represent the extracted spin states. We show that these states exhibit different forms of spin entanglement, whose detection is discussed in terms of the spin-squeezing inequalities.

We demonstrate behaviors of correlation effects in the calculations of atomic properties through two commonly employed many-body methods, namely the multiconfiguration Dirac-Hartree-Fock (MCDHF) and the relativistic coupled-cluster (RCC) methods. Particularly, we have benchmarked excitation energies, electric dipole (E1) matrix elements, magnetic dipole hyperfine structure constants ($A_{\text{hf}}$), and isotope shift (IS) constants in the singly ionized magnesium (${\mathrm{Mg}}^{+}$) systematically at different levels of approximation of both methods. We have also estimated the E1 polarizability of the ground state and lifetimes of the excited states using the E1 matrix elements from both methods. All these results are compared with the experimental values wherever available. We find that the computed results agree well with each other with a few exceptions; in particular, the $A_{\text{hf}}$ and IS constants from the RCC method are found to agree with the measurements better. This comparison analysis would be useful in evaluating the above-discussed properties in other atomic systems using the MCDHF and RCC methods more reliably.

We investigate the elastic and inelastic scattering of positrons by sodium atoms in both the ground state, $\mathrm{Na}\left(3s\right)$, and excited states, ${\mathrm{Na}}^{*}(3p, 4s, 3d)$, using the hyperspherical coordinate method with a model potential to represent the atomic core. The threshold behavior of positronium (Ps) formation cross sections is analyzed as the positron impact energy $E$ approaches zero. Within this framework, we derive a generalized expression for partial-wave Ps-formation cross sections at low positron energies, which applies to both ground-state and excited-state sodium targets. Our results confirm that the total threshold behavior follows the expected power-law dependence: ${\sigma }_{\text{Ps}}\propto E^{-1/2}$ for exothermic reactions and ${\sigma }_{\text{Ps}}\propto E^a$ for endothermic reactions, where $a>0$. Furthermore, we find that Ps-formation cross sections for positron scattering from excited Na states are significantly larger than those from the ground state in the low-energy region. A notable enhancement of Gailitis-Damburg oscillations is observed above the $\mathrm{Ps}(n=2)$ threshold, which may account for the increase observed in experimental data. Incorporating contributions from excited sodium targets improves agreement with experimental results and may help resolve discrepancies between theoretical predictions and measurements.

Between the absorption and the emission spectral line shapes of dense atomic and molecular media, such as dye solutions and alkali-noble buffer gas mixtures at high pressure, in many cases there exists a universal scaling, the Kennard-Stepanov relation, which is a manifestation of detailed balance. This relation plays a crucial role in recent Bose-Einstein condensation experiments of visible-spectral photons in, e.g., dye-solution-filled optical microcavities. It has recently been proposed to use high-pressure xenon–noble-gas mixtures as a thermalization medium for vacuum-ultraviolet regime photons, so as to extend the achievable wavelength range of such Bose-Einstein-condensed optical sources from the visible to the vacuum-ultraviolet regime. In this work, we report two-photon excitation spectroscopy measurements of ground-state ($5p^6$) xenon atoms subject to up to $80\mathrm{bar}$ of helium or krypton buffer gas pressure, respectively, in the 220–260 nm wavelength range. The study of such two-photon spectra is of interest, e.g., for the exploration of possible pumping schemes of a future vacuum-ultraviolet photon Bose-Einstein condensate. We have also recorded absorption and emission spectra of the $5p^6\leftrightarrow 5p^{5}6s$ single-photon transition near 147 nm wavelength of xenon atoms subject to $80\mathrm{bar}$ of krypton buffer gas pressure. We find that the ratio of absorption and emission shows a Kennard-Stepanov scaling, which suggests that such gas mixtures are promising candidates as a thermalization medium for a Bose-Einstein condensate of vacuum-ultraviolet photons.

We address the question whether hard-core bosons, equivalent to the XX model, remain integrable once the system is no longer closed. We consider the lattice version under incoherent local pump and loss and show, using random matrix theory, that the statistics of the complex spacial ratios indicate that the system is chaotic. Further, we show that the model belongs in the ${\mathrm{AI}}^{†}$ universality class of random matrices. In addition to this analysis, we investigate an emergent stripe pattern in the Lindbladian spectrum and relate it to the dissipative parameters of the model.

In the collective photon emission from atomic clouds both the atomic transition frequency and the decay rate are modified compared to a single isolated atom, leading to the effects of superradiance and subradiance. In this article, we analyze the properties of the Euclidean random matrix associated with the radiative dynamics of a cold atomic cloud, previously investigated in the contexts of photon localization and Dicke super- and subradiance. We present evidence of a phase transition, surprisingly controlled by the cooperativeness parameter, rather than the spatial density or the diagonal disorder. The numerical results corroborate the occurrence of such a phase transition at a critical value of the cooperativeness parameter, above which the lower edge of the spectrum vanishes, exhibiting a macroscopic accumulation of eigenvalues. Independent evaluations based on the two phenomena provide the same value for the critical cooperativeness parameter.

We provide a phase-space perspective for the analysis of the superfluid-insulator transition for finite-size Bose-Hubbard circuits. We explore how the eigenstates parametrically evolve as the interparticle interaction is varied, paying attention to the fingerprints of chaos at the quantum phase transition. Consequently, we demonstrate that the tomographic spectrum reflects the existence of mixed regions of chaos and quasiregular motion in phase space. This tomographic semiclassical approach is much more efficient and informative compared to the traditional level statistics inspection. Of particular interest is the characterization of the fluctuations that are exhibited by the many-body eigenstates. In this context, we associate with each eigenstate a Higgs measure for the identification of amplitude modes of the order parameter. Finally, we focus on the formation of the lowest Goldstone and Higgs bands.

A method to compute the excitation of narrow transitions at hard-x-ray energies by short focused x-ray pulses is developed. In particular, the effect of thin-film cavities on the pulse propagation is incorporated via a semianalytical algorithm requiring the numerical evaluation of only one two-dimensional Fourier transform. We investigate various limiting cases to confirm the reliability of the algorithm. As an application, we show how a focused x-ray pulse propagates in cavity structures utilized in previous theoretical studies and experiments with collimated beams.

Magnon blockade is a physical mechanism for the preparation of a single-magnon source, which has important applications in quantum information processing. Here we propose a scheme for generating an optimal magnon blockade in the spin-magnon quantum system. By introducing frequency detuning between the magnon and spin qubit of nitrogen-vacancy center, the conventional magnon blockade and the unconventional magnon blockade can be obtained under both strong and weak coupling, relaxing the requirements for coupling strength. Moreover, the conventional and unconventional magnon blockade can occur simultaneously when both the magnon and the spin qubit are driven. This allows the equal-time second-order correlation function to reach ${10}^{-8}$, about five orders of magnitude lower than that of the single conventional or unconventional magnon blockade. Additionally, the time-delayed second-order correlation function avoids oscillation. Our study demonstrates the impact of frequency detuning on the magnon blockade and proposes methods to enhance the magnon blockade and relax the requirements for coupling strength through frequency detuning.

We propose random non-Hermitian Hamiltonians to model the generic stochastic nonlinear dynamics of a quantum state in Hilbert space. Our approach features an underlying linearity in the dynamical equations, ensuring the applicability of techniques used for solving linear systems. Additionally, it offers the advantage of easily incorporating statistical symmetry, a generalization of explicit symmetry to stochastic processes. To demonstrate the utility of our approach, we apply it to describe real-time dynamics, starting from an initial symmetry-preserving state and evolving into a randomly distributed, symmetry-breaking final state. Our model serves as a quantum framework for the transition process, from disordered states to ordered ones, where symmetry is spontaneously broken.

Many quantum communication protocols rely on the distribution of entanglement between the different participating parties. One example is quantum key distribution (QKD), an application that has matured to commercial use in recent years. However, difficulties remain, especially with noise resilience and channel capacity in long-distance communication. One way to overcome these problems is to use high-dimensional entanglement, which has been shown to be more robust to noise and enables higher secret-key rates. It is therefore important to have access to certifiable high-dimensional entanglement sources to confidently implement these advanced QKD protocols. Here we develop a method for certifying high-dimensional time-bin entanglement in fiber-loop systems. In these systems, entanglement creation and detection can utilize the same physical components, and the number of time bins, and thus the entanglement dimension, can be adapted without making physical changes to the setup. Our certification method builds on previous proposals for the certification of angular-momentum entanglement in photon pairs. In particular, measurements in only two experimentally accessible bases are sufficient to obtain a lower bound on the entanglement dimension for both two- and multiphoton quantum states. Numerical simulations show that the method is robust against typical experimental noise effects and works well even with limited measurement statistics, thus establishing time-bin encoded photons as a promising platform for high-dimensional quantum-communication protocols.

We develop a method for visualizing the internal structure of multipartite entanglement in pure stabilizer states. Our algorithm graphically organizes the many-body correlations in a hierarchical structure. This provides a rich taxonomy from which one can simultaneously extract many quantitative features of a state including some traditional quantities such as entanglement depth, $k$-uniformity, and entanglement entropy. Our method also presents an alternative computational tool for extracting the exact entanglement depth and all separable partitions of a stabilizer state. Our construction is gauge invariant and goes beyond traditional entanglement measures by visually revealing how quantum information and entanglement is distributed. We use this tool to analyze the internal structures of prototypical stabilizer states (Greenberger-Horne-Zeilinger state, cluster state, stabilizer error correction codes) and are able to contrast the complexity of highly entangled volume law states generated by random unitary operators and random projective measurements.

Gaussian boson sampling (GBS), a computational problem conjectured to be hard to simulate on a classical machine, has been at the forefront of recent years' experimental and theoretical efforts to demonstrate quantum advantage. The classical intractability of the sampling task makes validating these experiments a challenging and essential undertaking. In this paper, we propose binned-detector probability distributions as a suitable quantity to statistically validate GBS experiments employing photon-number-resolving detectors. We develop the theoretical framework to compute such distributions by leveraging their connection with their respective characteristic function. The latter may be efficiently and analytically computed for squeezed input states as well as for relevant classical hypothesis like squashed states. Our theoretical framework encompasses other validation methods based on marginal distributions and correlation functions. Additionally, it can analytically accommodate various sources of noise, such as losses and partial distinguishability, a feature that has received limited attention within the GBS framework so far. We also derive how binned-detector probability distributions behave when Haar averaged over all possible interferometric networks, extending known results for Fock boson sampling.

We investigate the role of quadrature squeezing in the quantum teleportation protocol for coherent states using non-Gaussian resource states. For two-mode systems, the non-Gaussian resource states that we use are obtained with an experimentally realizable scheme of photon subtraction, photon addition, and photon catalysis on the two-mode squeezed vacuum and two-mode squeezed thermal states. We first analyze the nonclassical attribute of quadrature squeezing in these generated non-Gaussian states using the $\mathrm{U}\left(2\right)$-invariant squeezing approach, which allows us to account for all possible quadratures. We then show that the presence of such nonclassicality in non-Gaussian resource states is not necessary for successful quantum teleportation, a finding which is at variance with an earlier proposition in this direction. This result is important since it demonstrates how nonclassicality other than quadrature squeezing present in the resource can be utilized for quantum teleportation.