We present the results of our quantum annealing computations of the permanent electric dipole moments of several molecules. By applying an electric field as a perturbation and measuring the corresponding energy responses, the molecular electric dipole moments are obtained numerically through the finite field method. The ground-state electronic wave functions and energies are obtained using the quantum annealer eignsolver algorithm. This work provides a pathway for the computation of molecular properties in the quantum annealing paradigm.

Spin squeezing generated via interatom entanglement in multilevel atomic ensembles provides a powerful resource for quantum-enhanced metrology. Existing schemes that harness internal atomic degrees of freedom to boost squeezing typically encode the collective squeezing in complex superpositions of magnetic sublevels, which complicates state control and limits practical applications. Here, we propose a coherent control scheme that simultaneously enhances collective spin squeezing and maps the resulting atom-atom entanglement onto two well-defined magnetic sublevels suitable for subsequent metrology experiments. Our protocol sandwiches a quantum nondemolition measurement between two internal one-axis-twisting interactions arranged in an echo sequence. We show that this approach can optimally leverage internal states to boost the interatom entanglement and, at the same time, encode it in two magnetic sublevels, which is readily convertible into metrologically useful spin squeezing. Our results offer a straightforward and efficient strategy for generating highly entangled yet readily accessible quantum states in multilevel atomic systems.

This work attempts to present a complete theory of the $\mu \mathrm{H}$ hyperfine splitting, including all contributions above 1 ppm. Quantum electrodynamic and recoil corrections are calculated directly, while the proton structure correction is obtained with the help of the H hyperfine splitting. The resulting theoretical prediction for the ground state of $\mu \mathrm{H}$ is $E_{\mathrm{hfs}}=182626\left(5\right)\mu \mathrm{eV}$.

We establish a conservation law for the Quantum Fisher Information Matrix (QFIM) expressed as follows; when the QFIM is constructed from a set of observables closed under commutation, i.e., a Lie algebra, the spectrum of the QFIM is invariant under unitary dynamics generated by these same operators. Each Lie algebra therefore endows any quantum state with a fixed “budget” of metrological sensitivity—an intrinsic resource that we show, like optical squeezing in interferometry, cannot be amplified by symmetry-preserving operations. The Uhlmann curvature tensor naturally inherits the same symmetry group, and so quantum incompatibility is similarly fixed. As a result, a metrological analog to Liouville's theorem appears; statistical distances, volumes, and curvatures are invariant under the evolution generated by the Lie algebra. We discuss this as it relates to the quantum analogs of classical optimality criteria. This enables one to efficiently classify useful classes of quantum states at the level of Lie algebras through geometric invariants.

Any single on-off photocounter, which can only detect the presence or absence of photons without discriminating their number, is not capable of identifying the nonclassical nature of light. This limitation arises because any photocounting statistics obtained with such a detector can be easily reproduced with coherent states of a light mode. We show that a simple modification of an on-off detector—introducing controlled attenuation as a tunable setting—enables such detectors to reveal nonclassical properties of radiation fields.

The rate of $m$-photon transitions in matter, induced by an incident light field, depends on the field's $m\mathrm{th}$-order coherence function. Consequently, the coherence properties of the light field may be shaped to increase the rate of multiphoton transitions. Here, we determine the optimal state of a weak fixed-intensity, narrow-band incident light field, with a restricted maximal photon number, that optimally drives $m$-photon transitions in the case of a short-lived atomic multilevel system. We show that, in this case, no quantum properties of the light field need to be exploited, but that classical mixtures of coherent states are optimal.

It is important to improve the accuracy of quantum measurements and operations both in engineering and fundamental physics. It is known, however, that the achievable accuracy of measurements and unitary operations is generally limited by conservation laws according to the Wigner-Araki-Yanase theorem (WAY theorem) and its generalizations. Although many studies have extended the WAY theorem quantitatively, most of them, as well as the original WAY theorem, concern only additive conservation laws like the angular momentum conservation law. In this paper, we explore the limitation incurred by the energy conservation law, which is universal but is one of the nonadditive conservation laws. We present a lower bound for the error of a quantum measurement using a scattering process satisfying the energy conservation law. We obtain conditions that a control system Hamiltonian must fulfill in order to implement a controlled unitary gate with zero error when a scattering process is considered. We also show the quantitative relationship between the upper bound of the gate fidelity of a controlled unitary gate and the energy fluctuation of systems when a target system and a control system are both one qubit.

Quantum systems promise unprecedented performance with respect to classical counterparts for various applications involving sensing, communications, control, and computing. Bringing this promise to reality hinges upon the distinguishability between quantum states. This paper explores the distinguishability of a broad class of non-Gaussian states, namely the photon-varied Gaussian states (PVGSs), which can be generated with current technologies from Gaussian states of the electromagnetic field. First, we show that the problem of designing orthogonal PVGSs is tantamount to determining the algebraic varieties of generalized Hermite polynomials, thus bridging the fields of quantum mechanics and algebraic geometry. Then, we prove the existence of orthogonal PVGSs by showing that proper choices of the states' parameters lead to nonempty algebraic varieties. By exploiting the geometrical properties of such algebraic varieties, we also establish methodologies for designing pairs of orthogonal PVGSs. Finally, we explore the distinguishability of PVGSs undergoing noisy time evolution in the presence of decoherence and show that, in such conditions, the developed methodologies still allow for achieving the highest distinguishability. By bridging quantum mechanics and algebraic geometry, the findings of this paper provide insights into designing a new class of quantum states that are distinguishable.

We investigate how environment-induced interactions influence the entanglement dynamics of two atoms held at fixed positions near a perfectly reflecting boundary. Within the framework of open quantum systems, we explicitly incorporate the environment-induced energy shifts, including both atom-boundary contributions and an environment-induced atom-atom interaction, which are often neglected in previous studies. We show that, for any initial two-atom state, these energy-shift effects qualitatively and quantitatively modify the entanglement dynamics relative to treatments that omit them. Depending on the geometry and the parameter regime, the environment-induced interactions can either enhance entanglement generation—yielding a larger maximum concurrence and a longer entanglement lifetime—or suppress it, reducing both the peak concurrence and the survival time. This behavior contrasts sharply with the free-space case, where the environment-induced atom-atom interaction affects entanglement generation only for a restricted class of initial states and does so in an exclusively assisting manner.

Quantum state texture (QST), an emerging resource quantifying the global structural complexity of quantum states within a computational basis, exhibits dynamical behavior under relativistic frameworks that remains largely unexplored. This paper systematically investigates the evolution of QST under Lorentz boosts for single-particle and bipartite entangled Gaussian wave-packet systems. Based on Lorentz group representation theory and the Wigner rotation mechanism, we derive analytical expressions for the texture measure for both the single-particle and the bipartite entangled systems. The study reveals the following: (1) For a single-particle system, under the approximation that the wave-packet width is much smaller than the mass and the specific configuration where the initial momentum is perpendicular to the boost direction, both quantum coherence (QC) and QST remain invariant, determined solely by the initial spin angle, and the physical origin lies in the symmetry of the probability transfer between spin states induced by relativistic effects; (2) under the same approximations, for a bipartite entangled system, QC is conserved under arbitrary Lorentz boosts, while QST and quantum entanglement (QE) exhibit a competitive relationship with the relativistic effect parameter—QST increases monotonically with the parameter, whereas QE monotonically decays, and when both particles are Lorentz boosted simultaneously relativistic effects enhance the texture while further degrading entanglement compared to the single-particle boost scenario; (3) the reduced single-particle state obtained from the bipartite system exhibits texture and coherence that are completely unaffected by relativistic effects, indicating that the system's texture and overall coherence are stored within nonlocal correlations. To test the range of the narrow-packet approximation, we also evaluate the unexpanded Wigner-rotation integral numerically for finite widths $\sigma /m=0.2–0.4$, finding that the same monotonic trends persist while the second-order analytical formula mildly overestimates the exact integral. The sensitivity of QST to the phase distribution reorganization caused by Wigner rotations establishes it as an effective complementary resource for probing the fine phase structure of relativistic quantum systems, offering significant insights for quantum information processing in high-speed or noninertial frames.

The role of complex numbers in quantum theory extends beyond mathematical convenience, having recently been formalized as a resource under the framework of the resource theory of imaginarity. Operationally, imaginarity translates into using more resources in linear optical setups. In this work, we investigate the operational advantage offered by complex-valued measurements in the entanglement of assistance protocol for three-qubit systems. We demonstrate that employing such measurement bases leads to a significant improvement in the concentration of bipartite entanglement with the aid of the third party. We further analyze a modified entanglement swapping protocol and show that three-qubit complex measurement bases with certain symmetries outperform the standard Greenberger-Horne-Zeilinger basis. This is also one example where a three-qubit nonmaximally entangled basis surpasses a maximally entangled one in generating entanglement. Construction of the basis also addresses the open problems raised by Pimpel et al. [F. Pimpel et al., Phys. Rev. A 108, 022220 (2023)]. As an intriguing application, we show that using this approach in quantum network percolation on a honeycomb lattice reduces the required bond occupation probability by $22.7\%$ and the requirement of entanglement by $10.6\%$ in each bond.

We propose a protocol to realize arbitrary state synthesis and unitary operations on a qudit encoded in the collective dressed states of a Rydberg-blockaded array of three-level atoms. This system is isomorphic to the Jaynes-Cummings model and acts as a multilevel Rydberg superatom whose nonlinear spectrum can be precisely controlled through the parameters of the laser driving the intermediate-to-Rydberg transition. Control of the qudit state is possible through pulse sequences of the laser driving the ground-to-intermediate transition. The dimension of the qudit Hilbert space is scalable by adjusting the number of atoms involved in the Rydberg-blockaded array. We estimate the fidelity of our protocol for realizing arbitrary unitaries and discuss the influence of the finite lifetime of the Rydberg state. Our work paves the way for processing quantum information with Rydberg-blockaded arrays of atoms as an alternative to atom qubit arrays.

We investigate a quantum system consisting of two mirrors undergoing uniform acceleration in opposite directions and one or two stationary atoms localized in the right and left Rindler wedges, respectively. The system interacts with a scalar field described by plane-wave solutions in Rindler coordinates. We show that the combined effect of mirror-induced boundary conditions and the Unruh response leads to thermal factors together with spatial interference terms. In particular, the joint excitation probability exhibits enhancements beyond the product of individual probabilities, indicating field-mediated correlations across causally disconnected regions. These results provide insight into entanglement and decoherence in noninertial frames and are directly relevant to relativistic quantum information.

The spin Hall effect enables pure spin-current generation without charge transport. Notably, its intrinsic contribution, originating from spin-orbit coupling, can exhibit universal values that are robust against parameter fluctuations. Recent extensions of this effect to high-spin systems predict rich transport phenomena, including various high-rank spin tensor Hall currents. Here, we experimentally realize the intrinsic rank-2 spin tensor Hall effect in a spin-1 manifold of a single trapped ion by engineering effective spin tensor–momentum coupling in parameter space. We theoretically propose and experimentally observe that a controlled parameter quench produces the universal rank-2 spin tensor Hall effects, with measured conductivity of $0.93\left(18\right)q/8\pi$ close to the expected value of $q/8\pi$, while rank-1 spin vector and rank-zero charge currents vanish by symmetry. In contrast, a spin vector–momentum coupled model yields the conventional rank-1 conductivity of $0.79\left(8\right)q/4\pi$, close to the expected value of $q/4\pi$ with no tensor response. Our results establish trapped ions as a powerful platform for exploring higher-rank spin transport and open avenues for quantum simulations of exotic tensorial phenomena in high-spin systems.

The hadronic vacuum polarization (HVP) corrections to energy levels in muonic atoms are studied systematically across the periodic table. Two nuclear charge distribution models have been considered, with a partly analytical solution for a homogeneously charged sphere model and direct numerical integration for a Fermi nuclear charge distribution. Our comparison reveals a good agreement between both approaches with relative differences typically below a few percent. The magnitude of HVP corrections increases with nuclear charge, displaying irregularities that correlate directly with the nonmonotonic behavior of nuclear radii. Despite strong relativistic effects at high $Z$, the ratio of hadronic to muonic vacuum polarization remains remarkably stable, deviating by less than $10\%$ from the established $67\%$ nonrelativistic benchmark value.

We investigate the stability of current-carrying states with quasimomentum $K$ in the Bose-condensed phase of the hard-core Bose-Hubbard model on a square lattice, where particles transfer between two sites separated by distance $r$ with hopping amplitude decaying algebraically with $r$ as $\propto r^{-\alpha }$. Using a mean-field theory, we analyze the excitation spectrum and determine the critical quasimomenta associated with Landau and dynamical instabilities. We find that the long-range hopping suppresses the critical quasimomenta and makes them vanish at $\alpha =3$. Near $\alpha =3$, we show that the critical quasimomentum $K_{\mathrm{c}}$ for the dynamical instability exhibits the scaling behavior $K_{\mathrm{c}}\propto {\mathrm{\Delta }}^{1+\mathrm{\Delta }}$ with $\mathrm{\Delta }=\alpha -3$, where the scaling exponent explicitly depends on $\mathrm{\Delta }$, as a consequence of the long-range nature of the hopping.

We investigate a weakly interacting two-component Bose-Einstein condensate in the miscible regime in the presence of altermagnetism, i.e., a collinear and globally compensated magnetic order that breaks spin-rotation symmetry while maintaining zero net magnetization. Within Bogoliubov theory, we derive the quasiparticle spectrum and coherence factors and show that altermagnetic order generically induces an angular dependence of the low-energy excitations. As a result, the sound velocity, momentum-resolved magnetization in the quantum depletion, and density-spin response functions acquire anisotropic components. We show that these anisotropic contributions vanish after angular averaging, consistent with the defining feature of altermagnetism: nontrivial local spin polarization without a global magnetization. Finally, we evaluate the Lee-Huang-Yang correction to the ground-state energy in the altermagnetic phase. Our results should be testable with ultracold-atom experiments in the foreseeable future.

We investigate exceptional points of degeneracy (EPDs) in electromagnetic scattering of a sphere dimer from the electroquasistatic limit to the fully retarded regime. In the quasistatic limit, we prove that $\mathcal{P}\mathcal{T}$-symmetric configurations, realized by spheres with complex-conjugate susceptibilities, host EPDs. Beyond this limit, retardation breaks $\mathcal{PT}$ symmetry; nevertheless, by jointly tuning the material dispersions of the two spheres, we derive analytic synthesis conditions for realizing EPDs at real frequencies. Near an EPD, we show that single-parameter perturbations yield the characteristic square-root splitting of the eigenfrequencies, and we quantify its impact on scattering, extinction, and absorption, clarifying sensing implications.

We demonstrate a hybrid quantum memory that combines gradient echo memory (GEM) and electromagnetically induced transparency (EIT) protocols for reversible mapping between light and atomic coherence. By leveraging GEM and EIT complementarity, we realize time-to-frequency and frequency-to-time conversion mechanisms for spectrotemporal modes. This capability provides a versatile tool for quantum communication, where coherent frequency-time conversion enhances network interoperability. In addition, the protocol may enable fundamental studies of atomic coherence, including investigations of Rydberg polaritons and mapping of single Rydberg excitations and ionic impurities.