Classical public-key cryptography standards rely on the Rivest-Shamir-Adleman (RSA) encryption protocol. The security of this protocol is based on the exponential computational complexity of the most efficient classical algorithms for factoring large semiprime numbers into their two prime components. Here, we address RSA factorization building on Schnorr's mathematical framework where factorization translates into a combinatorial optimization problem. We solve the optimization task via tensor network methods, a quantum-inspired classical numerical technique. This tensor network Schnorr's sieving algorithm displays numerical evidence of polynomial scaling of resources with the bit-length of the semiprime. We factorize RSA numbers up to 100 bits and assess how computational resources scale through numerical simulations up to 130 bits, encoding the optimization problem in quantum systems with up to 256 qubits. Only the high-order polynomial scaling of the required resources limits the factorization of larger numbers. Although these results do not currently undermine the security of the present communication infrastructure, they strongly highlight the urgency of implementing postquantum cryptography or quantum key distribution.

Quantum shadow tomography based on the classical shadow representation provides an efficient way to estimate properties of an unknown quantum state without performing a full quantum state tomography. In scenarios where estimating the expectation values for only certain classes of observables is required, obtaining information about the entire density matrix is unnecessary. We propose a partial quantum shadow tomography protocol that estimates a subset of density-matrix elements relevant to the expectation values of structured observables. Specifically, we identify specific subsets of the tomographically complete set $\mathrm{Cl}{\left(2\right)}^{\otimes n}$ and a simple pseudo-inverse of the associated channel, which can be used to estimate all elements of the density matrix with the same active order. By restricting the protocol to smaller subsets of single-qubit Pauli measurements, it becomes experimentally more efficient. We demonstrate the advantage over unitary designs, such as the Clifford, full Pauli basis, and methods utilizing mutually unbiased bases, by analytically deriving error bounds and numerically evaluating the protocol on structured operators. We experimentally demonstrate the partial shadow estimation scheme for a wide class of two-qubit states (pure, entangled, and mixed) in the nuclear magnetic resonance (NMR) platform. The full density matrix, reconstructed experimentally by combining different partial estimators, achieves fidelities around 99%.

In this work, we examine the impact of imperfect randomness on the security of quantum key distribution (QKD) protocols with a set of linearly independent states, with particular emphasis on deviations from uniform a priori probabilities in quantum state preparation. Both stationary and nonstationary forms of randomness imperfections are considered. In the stationary case—where the preparation probabilities remain constant throughout the entire sequence—we demonstrate that increasing asymmetry monotonically decreases the source entropy and the Holevo information, thereby reducing the conditional entropy and the extractable secret key length. We also explicitly quantify the impact of preparation bias on the achievable secret key rate in protocols based on linearly independent states. In contrast, the non–independent and identically distributed regime, characterized by signalwise fluctuations in the a priori probabilities, is shown to yield a reduction in conditional entropy proportional to the second moment of the deviation distribution, assuming small perturbations. We further analyze several representative classes of biased distributions, establishing upper and lower bounds on the corresponding conditional entropies. These results highlight the necessity of rigorously accounting for randomness imperfections in practical QKD systems and suggest concrete strategies for adjusting key length estimation under realistic, nonideal conditions.

The quantum Zeno effect, arising from frequent measurements or strong system-environment interactions, has typically been considered difficult to actively control in point-like atomic systems. Here, we demonstrate tunable Zeno and anti-Zeno effects using a three-level giant atom configuration. By engineering the spatial arrangement of coupling points to introduce a controllable propagation phase, we generate coherent interference in quantum state evolution accompanied by significant non-Markovian dynamics. This approach enables the continuous modulation of the spontaneous emission rate from suppression to enhancement. Our work systematically reveals the fundamental physical mechanism of geometrically controlled quantum interference in light-matter interactions, offering insights for the design of novel quantum devices based on non-Markovian effects.

We put forward an approach to generate Wigner-negative states for field modes by engineering the field parity in driven-dissipative nonlinear systems. The parity of a radiation field is directly connected to its Wigner negativity, since the dominance of odd-parity Fock-state populations leads to a clear negative patch in the Wigner function, signaling the non-Gaussian nature of the state. Physically, the odd- or even-parity state associated with the corresponding population distribution can be modified by properly using the external coherent drive, along with incoherent excitation and dissipation. To elucidate this statement, we enumerate several typical systems in the presence of the drive or dissipation, targeted at transferring and trapping population in the odd-parity Fock-state subspace. Under reasonable experimental parameters, we confirm the steady-state Wigner negativity by simulations based on the Lindblad master equation, showing that the Wigner-negative effect is robust in the cases of odd-parity Fock-state population dominance. Our semianalytical estimates for the Wigner negativity agree quantitatively with the results of numerical simulations from the master equation. We also discuss the feasibility of implementing the proposed scheme on state-of-the-art superconducting-circuit architectures. This investigation opens a promising route to steady-state quantum non-Gaussian states and deepens insight into their nature.

We describe a phase-adjusted realification procedure that embeds any finite set of rays in ${\mathbb{C}}^3$ into ${\mathbb{R}}^6$. By assigning an appropriate phase to each ray before applying the standard coordinatewise map, we can arrange that two rays are orthogonal in ${\mathbb{C}}^3$ if and only if their images are orthogonal in ${\mathbb{R}}^6$, so the construction yields a faithful orthogonal representation of the original complex configuration. As a concrete example, we consider the 165 projectively distinct rays used in a ${\mathbb{C}}^3$ Kochen-Specker configuration obtained from mutually unbiased bases, list these 165 rays explicitly in ${\mathbb{C}}^3$, and give for each of them its image in ${\mathbb{R}}^6$ under the canonical realification map. We also note that, because the original three -element contexts are no longer maximal in ${\mathbb{R}}^6$, the embedded configuration admits two-valued states even though its realization with maximal contexts in ${\mathbb{C}}^3$ is Kochen-Specker uncolorable.

The notorious sign problem severely limits the applicability of quantum Monte Carlo simulations, as statistical errors grow exponentially with system size and inverse temperature. A recent proposal of a quantum-computing stochastic series expansion method suggested that the problem could be avoided by introducing constant energy shifts into the Hamiltonian. Here we critically examine this framework and show that it does not strictly resolve the sign problem for Hamiltonians with noncommuting terms. Instead, it provides a practical mitigation strategy that suppresses the occurrence of negative weights. Using the antiferromagnetic anisotropic XY chain as a test case, we analyze the dependence of the average sign on system size, temperature, anisotropy, and shift parameters. An operator contraction method is introduced to improve efficiency. Our results demonstrate that moderate shifts optimally balance sign mitigation and statistical accuracy, while large shifts amplify errors, leaving the sign problem unresolved but alleviated.

Rubidium energy levels for $n{}^{2}S$ ($n=14\text{–}20$), $n{}^{2}D$ ($n=12\text{–}20$), $n{}^{2}F$ ($n=9\text{–}32$), and $n{}^{2}G$ ($n=16\text{–}32$) are experimentally observed. Resonant two-photon spectroscopy is used to interrogate the high-lying $S$ and $D$ states, with $5{}^{2}P_{3/2}$ as the intermediate state. A multistep pump scheme is used to prepare $4{}^{2}D_{5/2}$, from which single-photon transitions to $F$ and $G$ are observed. The resulting uncertainties are series dependent but typically $<50\mathrm{MHz}$ (0.0017 ${\mathrm{cm}}^{-1}$), limited mainly by the residual width of the line shape. Quantum defects for all series are consistent with prior literature values. The precision of this work is not sufficient to update the ionization energy.

The rapid turn-on of a strong, resonant, continuous wave laser field may trigger the formation of a transient oscillation akin to a train of damped solitons, before the vapor-field system relaxes into a stationary state. We study this transient dynamic on theoretical models of a rubidium vapor. We also consider doubly resonant V systems, for which the transients take the form of trains of damped simultons. We compute the propagating field(s) by solving the Maxwell-Bloch equations, taking homogeneous broadening, Doppler broadening and the full hyperfine structure of the atoms into account. We also compare the actual fields to the stationary dnoidal fields predicted by the Maxwell-Bloch equations in conditions of self-induced transparency. A similar dynamics is expected to occur in any atomic vapor at the turn-on of a strong resonant continuous wave field provided the turn-on is sufficiently fast compared to relaxation.

We present the design and characterization of a laser pulse shaper, which creates an “ultraslow optical centrifuge”—a linearly polarized field the polarization vector of which rotates with arbitrarily low angular acceleration. By directly recording this rotation in time with nonlinear cross-correlation, we demonstrate the tunability of the initial and final rotational frequencies of such a centrifuge in the range of accelerations, which are three orders of magnitude lower than those available with a conventional centrifuge design. We showcase the functionality of the ultraslow centrifuge by spinning ${\mathrm{CS}}_2$ molecules in a molecular jet. Utilizing the extremely low angular acceleration to control molecular rotation inside viscous media is a promising application for this unique optical tool.

We present a generalization of the semiclassical theory of tunneling of electrons from deeply bound states in highly charged ions subject to a static electromagnetic field of extreme strength [J. Exp. Theor. Phys. 87, 433 (1998)] to the case where the electric and magnetic fields are of an arbitrary relative amplitude and directed at an arbitrary angle. The obtained result accounts for the Coulomb interaction and spin precession. Derived formulas can be used for the calculation of ionization rates in tightly focused laser pulses of multipetawatt and exawatt power. We demonstrate application of the rates for the analysis of tunnel ionization of H-like ions of xenon and radon at intensities above ${10}^{24}\mathrm{W}/{\mathrm{cm}}^2$.

Laguerre-Gaussian (LG) wave packets, known for their vortex structure and nonzero orbital angular momentum (OAM), are of great interest in various scientific fields. Here we study the nonrelativistic dynamics of a spatially localized electron LG wave packet interacting with an inhomogeneous external electric field that violates the axial symmetry of the initial wave function. We focus on the analysis of the electron density and demonstrate how it is affected by the external field. Within the first order of perturbation theory, we calculate the electron wave function and reveal that the electric field may significantly alter the wave packet's structure and distort its qualitative form. We demonstrate that, due to the interaction with the external field, the degenerate zeros of the initial wave function located on the $z$ axis split into multiple nondegenerate nodes in the transverse plane representing separate single-charge vortices. This mechanism resembles the analogous effects known in topological optics. These findings provide new insights into controlling and manipulating twisted matter beams and into their possible instabilities.

We present a laser architecture generating dissipative optical solitons whose temporal profile consists of a central body flanked by intense functional sidelobes. The soliton phase profile features a phase difference of the order of $\pi$ between the central body and the first-order sidelobes. The sprawling structure of this soliton with an alternating phase profile provides extended interaction capabilities, entailing the formation of optical soliton molecules with predetermined internal separations. We show numerically and experimentally that these “tentacle” soliton structures are generated from a fiber laser cavity combining dispersion management with adjustable spectral filtering.

We investigate the Rice-Mele model with on-cell Kerr-type nonlinearities, where the interaction depends on the total particle number within each unit cell rather than on individual sites. This interaction enables a nontrivial interplay between topology and nonlinear dynamics in soliton pumping. In the weakly interacting regime, the ground-state soliton undergoes quantized Thouless pumping. At intermediate interaction strengths, soliton creation and annihilation break adiabaticity and disrupt quantized transport. In the strong-coupling regime, the coexistence of ground- and excited-state solitons leads to negligible coupling at energy crossings, giving rise to discrete time-translation symmetry breaking (DTTSB) in the soliton dynamics. Comparison of mean-field results with exact diagonalization along closed circular pumping paths confirms both the validity of the mean-field description and the robustness of DTTSB across different pumping trajectories. Our findings reveal how interaction-induced effects can fundamentally modify topological transport and suggest that these phenomena may be explored in cold-atom, photonic, and superconducting-circuit platforms.

We investigate the single-photon scattering spectrum of a driven $\mathrm{\Lambda }$-type giant-atom system chirally coupled to a one-dimensional waveguide. By employing a real-space scattering approach, we obtain analytical solutions for the scattering amplitudes that remain valid in both Markovian and non-Markovian regimes. We observe that an external driving field induces a splitting of the transmission spectrum's dip into double dips, with the distance between the two dips increasing as the strength of the driving field increases. The chiral nature of the coupling allows for controlled switching between complete transmission and perfect reflection of incident photons. We find robust perfect transmission at specific phase values, independent of the driving field parameters. Moreover, in the non-Markovian regime, as the size of the giant atom increases, the oscillatory behavior of the scattering spectrum becomes more pronounced. Adjusting the giant-atom size enables control over the number of decoupling points as well as the number of complete reflection points.

The challenge of understanding quantum measurement persists as a fundamental issue in modern physics. Particularly, the abrupt and energy-nonconserving collapse of the wave function appears to contradict classical thermodynamic laws. The contradiction can be resolved by considering measurement itself to be an entropy-increasing process, driven by the second law of thermodynamics. One such resolution explains the apparently irreversible emergence of objective outcomes in an isolated, unitarily evolving quantum system via the theory of closed-system equilibration. Working within this framework, we construct the set of “objectifying observables” that best encode the measurement statistics of a system in an objective manner and establish a measurement error bound to quantify the probability an observer will obtain an incorrect measurement outcome. Using this error bound, we show that the objectifying observables readily equilibrate on average under the set of Hamiltonians which preserve the outcome statistics on the measured system. Using a random matrix model for this set, we numerically determine the measurement error bound, finding that the error only approaches zero with increasing environment size when the environment is coarse grained into so-called observer systems. This indicates the necessity of coarse graining an environment for the emergence of objective, classical measurement outcomes.

The Rayleigh criterion has long served as a fundamental limit for the resolution of optical imaging. Recent advances in multiparameter quantum metrology have led to quantum superresolution that can break this limit and achieve nonvanishing precision in estimating the separation between a pair of closely located incoherent point sources. For two-dimensional optical systems, the quantum superresolution has been studied for the Cartesian components of separation between two incoherent point sources. However, the precision limit of estimating the full distance between two point sources remains unknown so far. In this paper, we investigate the estimation precision of the full distance between two incoherent point sources with arbitrary intensities in a two-dimensional imaging system. Through the multiparameter quantum estimation theory, we obtain the ultimate estimation precision for the distance and show that it remains nonzero when the distance approaches zero, which surpasses the Rayleigh criterion. We further show the dependence of the estimation precision on the relative orientation between the two point sources, which leads to a scheme that can enhance the precision by aligning the sources along proper directions if the point-spread functions are not circularly symmetric, and the enhancement is determined by the extent to which the point-spread functions deviate from circular symmetry. Finally, the results are illustrated by incoherent sources with Gaussian point-spread functions.

The quantum approximate optimization algorithm (QAOA) has been suggested as a promising candidate for the solution of combinatorial optimization problems. Yet, whether—or under what conditions—it may offer an advantage compared with classical algorithms remains to be proven. Using the standard variational form of QAOA requires a high number of circuit parameters that have to be optimized at a sufficiently large depth, which constitutes a bottleneck for achieving a potential scaling advantage. The linear-ramp QAOA has been proposed to address this issue, as it relies on only two parameters that have to be optimized. Based on this, we develop a method to estimate suitable values for those parameters through extrapolation, starting from smaller problem sizes (number of qubits) toward larger problem sizes. We apply this method to several use cases, such as portfolio optimization, feature selection, clustering, and weighted maxcut. From results obtained on a noiseless quantum emulator, we evaluate the quantum runtime scaling for finding the optimal solution and compare it with that of classical methods. In the case of portfolio optimization, we demonstrate superior scaling compared with the classical runtime for the problem sizes of up to 28 qubits that we consider in this work.

Simulating large quantum circuits on hardware with limited qubit counts is often attempted through methods like circuit knitting, which typically incur sample costs that grow exponentially with the number of connections cut. In this work, we introduce a framework based on cluster-level light-cone analysis that leverages the natural locality of quantum workloads. We propose two complementary algorithms: the causal decoupling algorithm, which exploits geometric disconnections in the light cone for sampling efficiency, and the algebraic decomposition algorithm, which utilizes algebraic expansion to minimize hardware requirements. These methods allow simulation costs to depend on circuit depth and connectivity rather than system size. Together, our results generalize Lieb-Robinson–inspired locality to modular architectures and establish a quantitative framework for probing local physics on near-term quantum devices by decoupling the simulation cost from the global system size.

Understanding and classifying multipartite entanglement are fundamental to quantum information processing. This work focuses on absolutely maximally entangled (AME) states, a class of highly entangled states characterized by their maximal entanglement across any bipartitions. To analyze and classify AME states, we employ the minimal decomposition entropy, defined as the minimum Rényi entropy $S_q$ associated with the state's decomposition over all local product bases. This quantity identifies the product bases in which the state is maximally localized, thereby yielding optimal representations for analyzing properties of AME states. We develop an efficient algorithm for computing the minimal decomposition entropy for finite $q>1$ and compare AME and Haar-random states for $q=2$ and $q=\infty$ in qubit, qutrit, and ququad systems. For $q=2$, AME states of four qutrits and ququads show lower minimal entropy than generic states, indicating sparser optimal forms. For $q=\infty$, related to the geometric measure of entanglement, AME states exhibit higher entanglement. The algorithm also simplifies known AME states into sparser representations, aiding in distinguishing genuinely quantum AME states from those constructible from classical combinatorial designs. Our results advance the classification of AME states and demonstrate the utility of minimal decomposition entropy as both a local unitary invariant and a tool for state simplification.