We show that virtual particles, despite being unobservable, can be described by quantum operators which can be interpreted under certain conditions as valid qubit quantum states. For a single virtual fermion, we prove that such a state is a separable mixed two-qubit state with a well-defined finite temperature. For spin-1 virtual bosons, we find them to be associated with four-qubit operators which can be interpreted as quantum states for some gauges. We also study the creation of virtual pairs of fermions, where the pair is shown to be associated with an entangled four-qubit operator, and show the corresponding quantum circuit. Finally, we prove that renormalization does not structurally affect these results. These findings represent interesting connections between quantum field theory, quantum information, and quantum thermodynamics.

We introduce and analyze approximate quantum secret sharing in a formal cryptographic setting, wherein a dealer encodes and distributes a quantum secret to players such that authorized structures (sets of subsets of players) can approximately reconstruct the quantum secret and omnipotent adversarial agents controlling nonauthorized subsets of players are approximately denied the quantum secret. In particular, viewing the map encoding the quantum secret shares for players in an authorized structure as a quantum channel, we show that approximate reconstructability of the quantum secret by these players is possible if and only if the information leakage, given in terms of a certain entanglement-assisted capacity of the complementary quantum channel to the players outside the structure and the environment, is small.

By incorporating the quantum effects and the Coulomb interaction between the first ionized electron and the residual ion in a uniform theory, the Coulomb-corrected quantum-trajectories (CCQT) method is developed to describe the recollision-impact ionization (RII) process in nonsequential double ionization of atoms in intense laser field. The results simulated by CCQT are found to be in better agreement with the experimental results, compared with those calculated by the classical-trajectory Monte Carlo (CTMC) and strong-field approximation (SFA) methods. Considering its advantage of small computational cost and back-trajectory analysis, the CCQT method will be an efficient theoretical tool to quantitatively investigate the underlying physics of the complex and coherent multielectron dynamics in intense laser field.

Moiré lattices are aperiodic systems formed by a superposition of two periodic lattices with a relative rotational angle. In optics, the photonic moiré lattice has many appealing properties such as its ability to localize light, thus attracting much attention on exploring features of such a structure. One fundamental research area for photonic moiré lattices is the properties of eigenstates, particularly the existence of localized eigenstates and the localization-to-delocalization transition in the energy band structure. Here we propose an accurate algorithm for the eigenproblems of aperiodic systems by combining plane-wave discretization and spectral indicator validation under the higher-dimensional projection, allowing us to explore energy bands of fully aperiodic systems. A localization-delocalization transition regarding the intensity of the aperiodic potential is observed and a Pythagoras superposition principle for localized eigenstates of two-dimensional moiré lattices is revealed by analyzing the relationship between the aperiodic system and its corresponding periodic eigenstates. This principle sheds light on exploring the physics of localizations for moiré lattices.

As one of the most remarkable features of quantum mechanics, quantum coherence is regarded as an invaluable quantum resource in quantum information. Using the optical fiber as one of the effective quantum channels, the remote distribution of quantum coherence through fiber is essential for potential practical applications. Here we propose the remote distribution scheme of the quantum coherence resource through an optical fiber. The two-mode squeezed state (TMSS) generated by the nondegenerate optical parametric amplifier is distributed through optical fibers, and the quantum coherence of the TMSS is analyzed by the relative entropy of the covariance matrix. We show that quantum coherence is robust against the distribution distance even if the entanglement disappears at short distribution distance due to the loss and excess noise in fiber channels. Our results provide a direct reference for the potential practical applications of quantum coherence.

In this paper, we report findings of nonstationary behavior observed in a fully connected qubit network, utilizing a random unitary evolution model in open quantum system theory. The environmental effect is reflected in the partial swap interaction between pairs of qubits with a certain probability. Our study begins with a simple Ising-type Hamiltonian and through many iterations of random unitary evolution, a nonstationary oscillatory state may arise, which encodes certain memory of the initial state. The nontrivial periodic motion of some local observables is indicative of a continuous time crystal phase. We also explore the extension of our study to other types of Hamiltonians and demonstrate that this nonstationary behavior is widespread in our model due to the generalized dynamical symmetry. Remarkably, both theoretical and numerical analysis support the robustness of the constructed time crystal phase to most types of noise. Our research provides a perspective for constructing the time-crystal phase in an open system model.

We investigate the exact master equation of Hu, Paz, and Zhang for a quantum harmonic oscillator at zero temperature with a Lorentz-Drude type Ohmic spectral density. This master equation plays an important role in the study of quantum Brownian motion and in various applications. In this paper, we give an analytical evaluation of the coefficients of this non-Markovian master equation without Lindblad form, which allows us to investigate consistencies of the solutions, the positivity of the stationary density operator, and the boundaries of the model's parameters.

Entropic uncertainty relations demonstrate the intrinsic uncertainty of nature from an information-theory perspective. Recently, a quantum-memory-assisted entropic uncertainty relation for multiple measurements was proposed by Wu et al. [Phys. Rev. A 106, 062219 (2022)]. Interestingly, the quantum-memory-assisted entropic uncertainty relation for multiple measurement settings can be further generalized. In this work, we propose two complementary multipartite quantum-memory-assisted entropic uncertainty relations and our lower bounds depend on values of complementarity of the observables, (conditional) von Neumann entropies, Holevo quantities, and mutual information. As an illustration, we provide several typical cases to exhibit that our bounds are tighter and outperform the previous bounds.

Entanglement and uncertainty relation are two focuses of quantum theory. We relate entanglement sharing to the entropic uncertainty relation in a $(d\times d)$-dimensional system via weak measurements with different pointers. We consider both the scenarios of one-sided sequential measurements in which the entangled pair is distributed to multiple Alices and one Bob and two-sided sequential measurements in which the entangled pair is distributed to multiple Alices and Bobs. It is found that the maximum number of observers sharing the entanglement strongly depends on the measurement scenarios, the pointer states of the apparatus, and the local dimension $d$ of each subsystem, while the required minimum measurement precision to achieve entanglement sharing decreases to its asymptotic value with the increase of $d$. The maximum number of observers remain unaltered even when the state is not maximally entangled but has strong-enough entanglement.

The autoionization of core-excited Rydberg states is theoretically studied for a broad range of principal and angular-momentum quantum numbers $n$ and $l$ in alkaline-earth-metal atoms. We combined two theoretical methods to calculate accurate autoionization rates for $n=10-65$ and $l=0-45$ over the 100 orders of magnitude that they span. The strong interaction between the two valence electrons for low $l$ states is treated from first principles with configuration interaction with exterior complex scaling, while at large $l$ the weak correlation is described by a perturbative approach and arbitrary-precision floating-point arithmetics. The results, which we benchmark against available experimental data, provide autoionization rates for the $N{p}_{1/2,3/2}$ and, when applicable, $(N-1)d_{3/2,5/2}$ ion-core states of Mg, Ca, and Sr $(N=3-5)$. Using the extensive set of calculated data, we analyze the dependence of the rates on $l$ and identify five general laws of the autoionization of high-$l$ states. An empirical formula describing the scaling of the rates with $l$ is suggested.

We theoretically study the influence of molecular alignment on the attosecond photoionization of the ${\mathrm{N}}_2$ molecule. Based on the numerical simulations of the single-active-electron two-dimensional time-dependent Schrödinger equation, we find that the alignment-averaged photoelectron momentum distributions deviate from the single-molecule result, especially for a large molecular alignment angle and a low degree of molecular alignment. As a result, the photoemission time delays extracted from the angular-averaged streaking spectra are different from the single-molecule result. More importantly, the alignment-averaged photoemission time delays are found to depend on the degree of molecular alignment as well as the molecular alignment distribution. Our results reveal the important role of molecular alignment in the molecular attosecond photoionization.

As a step toward the full ab initio description of two-photon double ionization processes, we present a finite-pulse version of the virtual-sequential model for polyelectronic atoms. The model relies on the ab initio description of the single ionization scattering states of both the neutral and ionized target system. As a proof of principle and a benchmark, the model is applied to the helium atom using the newstock atomic photoionization code. The results of angularly integrated observables, which are in excellent agreement with existing time-dependent Schrödinger equation (TDSE) simulations, show how the model is able to capture the role of electron correlation in the nonsequential regime, and the influence of autoionizing states in the sequential regime, at a comparatively modest computational cost. The model also reproduces the two-particle interference with ultrashort pulses, which is within reach of current experimental technologies. Furthermore, the model shows the modulation of the joint energy distribution in the vicinity of autoionizing states, which can be probed with extreme-ultraviolet pulses of duration much longer than the characteristic lifetime of the resonance. The formalism discussed here applies also to polyelectronic atoms and molecules, thus opening a window on nonsequential and sequential double ionization in these more complex systems.

Non-Efimovian $N$-body resonances are investigated in the regime of a large two-body $s$-wave scattering length. In view of a universal description of low-energy bound and quasibound states, a contact model is introduced. The modeling requires two parameters in addition to the scattering length. Using a modified scalar product, the contact model provides a normalization of bound states, possibly not square integrable, that coincides with that of the corresponding finite range model.

We investigate the topological amplification and frequency conversion of a one-dimensional photonic lattice subjected to a two-photon driving, considering both the thermodynamic- and dynamical-stability regimes. Our analysis shows that the critical behavior of their stability occurring at zero energy depends on the width of the lower band, as well as the strength and phase of the two-photon driving. We demonstrate that the presence of the driving field does not alter the band topology of the system under both regimes, and we showcase the nontrivial band topology. The occurrence of edge modes within the band gap is also demonstrated by employing a Bogoliubov (squeezed-state) representation. Furthermore, we show the amplification and frequency conversion of edge modes using the input-output formalism, relying on the mechanism of an optical parametric amplifier. These phenomena exhibit an absence-to-presence transition at a critical value of hopping strength, signifying a topological phase transition. Additionally, we demonstrate the robustness of these phenomena against symmetry-preserving disorders. Our findings have potential applications in engineering fault-tolerant quantum-optics devices based on the topological protection.

The retrieval of the phase with single-photon states is a fundamentally and technically challenging endeavor. Here we report an experimental realization of hologram recordings with heralded single-photon illumination and continuous observation of photon statistics. Thereby, we demonstrate the basic principle of holography with single-photon states which cannot be described with the classical wave theory. Under conditions with illumination more than 200 times weaker than the noise of the detector, a hologram (interferogram) recorded with a heralded single-photon source revealed an object not visible with nonheralded illumination and slightly higher intensity. The dramatic improvement in retrieval of amplitude and phase information achieved with the heralded single-photon source can be explained by the strong suppression of noise due to the nonclassical temporal correlation between twin photons and the small coincidence time window. The method could be useful for recording and retrieving amplitude and phase information in the presence of strong noise, for covert imaging, and for imaging of photosensitive biological and material samples.

We apply the stochastic Schrödinger equation approach to study the non-Markovian dynamics of quantum systems coupled to a squeezed environment. We derive the non-Markovian quantum-state-diffusion equation using coherent-state unraveling and the associated zeroth-order master equation for general models in a microscopic quantum context. Focused on a dissipative optical cavity coupled with a squeezed vacuum, the numerical simulations demonstrate the time evolution of photon numbers in an optical cavity. We observe that the long-time limits of the non-Markovian dynamics are significantly different from those of the Markovian dynamics for various memory factors and squeezing factors. Additionally, non-Markovian dynamics exhibit a distinct pattern of behavior when parameters change. Our work provides a method to study the impact of multiple parameters on the non-Markovian dynamics and long-time limits in a joint manner. The method can be further extended to squeezed finite-temperature environments.

In contrast to the determinant, no algorithm is known for the exact determination of the permanent of a square matrix that runs in time polynomial in its dimension. Consequently, noninteracting fermions are classically efficiently simulatable while noninteracting bosons are not, underpinning quantum supremacy arguments for sampling the output distribution of photon interferometer arrays. This work introduces a graph-theoretic framework that bridges both the determinant and permanent. The only nonzero eigenvalues of a sparse non-Hermitian operator $\breve{M}$ for $n$ spin-$1/2$ particles are the $n\mathrm{th}$ roots of the permanent or determinant of an $n\times n$ matrix $M$, interpreting basis states as bosonic or fermionic occupation states, respectively. This operator can be used to design a simple and straightforward method for the classical determination of the permanent that matches the efficiency of the best-known algorithm. Gauss-Jordan elimination for the determinant of $M$ is then equivalent to the successive removal of the generalized zero eigenspace of the fermionic $\breve{M}$, equivalent to the deletion of some nodes and reweighting of the remaining edges in the graph such that only $n$ nodes survive after the last step. In the bosonic case, the successive removal of generalized zero eigenspaces for $\breve{M}$ is also equivalent to node deletion, but new edges are added during this process, which gives rise to the higher complexity of computing the permanent. Our analysis may point the way to new strategies for classical and quantum evaluation of the permanent.

All matter is made up of fermions, one of the fundamental type of particles in nature. Fermions follow the Pauli exclusion principle, stating that two or more identical fermions cannot occupy the same quantum state. Antisymmetry of the fermionic wave function, however, implies additional constraints on the natural occupation numbers. These constraints depend on the dimensionality and purity of the system and have so far not been explored experimentally in a fermionic system to our best knowledge. Here we propose an experiment in a multi-quantum-dot system capable of producing the highly entangled fermionic states necessary to reach the regime, where these additional constraints become dominant and can be probed. The type and strength of the required multifermion entanglement provides barriers to reaching deep into this regime. Transcending these barriers thus serves as a testing ground for the capabilities of future fermionic quantum information processing as well as quantum computer architectures based on fermionic states. All operations in our proposal are based on all-optical gates presented in Li and Akopian [arXiv:2107.05960 (2021)]. We simulate our state preparation procedures in realistic structures, including all main decoherence sources, and find fidelities above 0.97.

Being able to reliably transfer the quantum state from one system to another is crucial to developing quantum networks. A standard way to accomplish this transfer of information is by making use of an intermediate information carrier (e.g., a photon) that is emitted by the first system and absorbed by the second. For such a scenario one can develop an effective description by eliminating the intermediate degrees of freedom, which yields an effective direct coupling between the two systems. If, however, the spectral properties of the two systems are different, the photon's time-frequency shape needs to be appropriately modified before it reaches the second system. We study here the effective description that results when we thus manipulate the intermediate photon. We examine a unitary transformation $U$ that time reverses, frequency translates, and stretches the photon wave packet. We find that the concomitant modifications to the effective description can best be understood in terms of a change to the state's time argument $\rho \left(t\right)={\rho }_1\left(\tilde{t}\right)\otimes {\rho }_2\left(t\right)$, where $\tilde{t}$ is a fictitious time for the first system that is stretched and runs backward. We apply this theory to three-level $\mathrm{\Lambda }$ systems inside optical cavities, and we numerically illustrate how performing the unitary transformation $U$ results in improved quantum state transfer.