The uncertainty relations (URs) of two arbitrary Hermitian and non-Hermitian incompatible operators represented by the product of variances have been confirmed theoretically and experimentally in various physical systems. However, the lower bound of the product uncertainty inequality can be null even for two noncommuting operators, i.e., a trivial case. Therefore, for two incompatible operators over the measured system state, the associated URs regarding the sum of variances are valid in a state-dependent manner, and the lower bound is guaranteed to be nontrivial. Although the sum URs formulated for Hermitian and unitary operators have been affirmed, the general forms for arbitrary non-Hermitian operators have not yet been investigated. This study presents the sum URs for non-Hermitian operators acting on system states using an appropriate Hilbert-space metric. The compatible forms of our sum inequalities with the conventional quantum mechanics are also provided via the $G$-metric formalism. Concrete examples illustrate the validity of the proposed sum URs in both $\mathcal{PT}$-symmetric and $\mathcal{PT}$-broken phases. The developed methods and results can help give an in-depth understanding of the usefulness of $G$-metric formalism in non-Hermitian quantum mechanics and the sum URs of incompatible operators within.

Recent results on electron tunneling across a potential barrier, inferred from observations or obtained from theoretical models, have suggested superluminal or instantaneous barrier traversal times. In this work we investigate relativistic wave-packet dynamics for an electron tunneling through a potential barrier employing space-time resolved solutions to relativistic quantum field theory (QFT) equations. We prove by linking the QFT property of microcausality to the wave-packet behavior that the tunneling dynamics is fully causal, precluding instantaneous or superluminal effects. We illustrate these results by performing numerical computations for an electron tunneling through a potential barrier for standard tunneling as well for Klein tunneling. In all cases (Klein tunneling or regular tunneling across a standard or a supercritical potential) the transmitted wave packet remains in the causal envelope of the propagator, even when its average position lies ahead of the average position of the corresponding freely propagated wave packet.

The challenge of determining bounds for the minimal number of vectors in a three-dimensional Kochen-Specker (KS) set has captivated the quantum foundations community for decades. This paper establishes a weak lower bound of 10 vectors, which does not surpass the current best-known bound of 24 vectors. By exploring the complementary concept of large non-KS sets and employing a probability argument independent of the graph structure of KS sets, we introduce a technique that could be applied in the future to derive tighter bounds. Additionally, we highlight an intriguing connection to a generalization of the moving sofa problem in navigating a right-angled hallway on the surface of a two-dimensional sphere.

Quantum channel coding is an effective method to reduce noise interference in quantum communication and has been extensively investigated both theoretically and practically. It is difficult, however, for ordinary channel-coding strategies to deal with scenarios in which quantum noises are completely or partially unknown. This paper introduces a solution using an equivariant variational quantum algorithm to design coding schemes for unknown channels. Our approach employs parameterized quantum channels within an equivariant Ansatz. We analyze the channel's capabilities, demonstrate the mitigation of the barren plateau, and provide convergence guarantees for our method. The numerical results highlight the following: (1) Our method achieves higher fidelity and faster convergence than naive methods in various quantum communication scenarios. (2) The equivariant method exhibits enhanced convergence and trainability, efficiently avoiding the barren-plateau issue.

We propose a variational approach to explore quasiparticle excitations in interacting quantum many-body systems, motivated by the potential in leveraging near-term noisy intermediate scale quantum devices for quantum-state preparation. By exploiting translation invariance and potentially other Abelian symmetries of the many-body Hamiltonian, we extend the variational quantum eigensolver (VQE) approach to construct spatially localized quasiparticle states that encode information on the whole excited band, allowing us to achieve quantum parallelism. We benchmark the proposed algorithm via numerical simulations performed on the one-dimension transverse field Ising chain. Our numerical results demonstrate that VQE can capture both the magnon quasiparticles of the paramagnetic phase, and the topologically nontrivial domain wall excitations in the ferromagnetic regime. We argue that the localized quasiparticle states constructed with VQE contain accessible information on the full band of quasiparticles, and provide valuable insight into the way interactions renormalize the bare spin flip or domain wall excitations of the simple, trivially solvable limits of the model. These results serve as important theoretical input towards utilizing quantum simulators to directly access the quasiparticles of strongly interacting quantum systems, as well as to gain insight into crucial experimentally measured properties directly determined by the nature of these quasiparticles.

Spin-orbit (SO) splitting in open-shell diatomic molecules gives rise to unique doublet electronic states and a wide range of rotational spectra. In spite of high importance of SO effect its manifestation at interaction with ultrashort and intense ultraviolet (UV) laser pulses is weakly studied. Our simulations confirm clearly manifestations of nonlinear phenomena in SO-splitting fragment spectra as the UV pulse intensity increases. These nonlinear effects in kinetic energy release and photofragment angular distribution spectra clearly reflect the SO splitting of the $\mathrm{\Pi }$ state and the $\mathbf{R}\text{−}\mathrm{\Omega }$ coupling ($\mathbf{R}$ is the nuclear rotational angular momentum and $\mathrm{\Omega }=\mathrm{\Lambda }+\mathrm{\Sigma }$ is the projection of total angular momentum on the molecule axis). We show that in case of nonresolved rotational excitation the $\mathbf{R}\text{−}\mathrm{\Omega }$ coupling on doublet-state transitions can be effectively approximated as the $\mathbf{R}\text{−}\mathrm{\Lambda }$ coupling, as for a singlet state, yet including actual SO splitting on the potential energy curve of the doublet $\mathrm{\Pi }$ state. The present investigation not only reveals the nonlinear SO-splitting effects on photodissociation dynamics induced by intense UV pulses, but also provides practical approaches for efficient modeling of the photoinduced ultrafast nuclear dynamics incorporating the SO-splitting phenomena.

We consider a foundational question in energy harvesting: Given a partly random energy source, is it possible to extract the energy without also transferring randomness or accepting another thermodynamical cost? We answer this in the positive, describing scenarios and protocols where in principle energy is extracted from a field with randomness but without any randomness being transferred and without energy dissipation. We explain why these protocols do not violate basic physical principles. Such protocols fundamentally outperform existing methods of rectification which dissipate power or demonlike feedback protocols which transfer randomness to the feedback system. The protocols exploit the possibility of the harvesting system taking several trajectories that lead to the same final state at a given time. A key example involves Rabi oscillations between energy levels, exploiting the multitude of rotation axes in the state space. The quantum system is deterministically excited to the highest energy level after interacting with the source for a fixed amount of time, irrespective of the random initial phase of the external potential. These realizations show the value of Rabi-oscillation-type techniques for enhancing energy harvesting.

Correlation is the basic mechanism of every measurement model, as one never accesses the measured system directly. Instead, correlations are created, codifying information about the measurable property into the environment. Here, we address the problem of the emergence of physical reality from the quantum world by introducing a model that interpolates between weak and strong nonselective measurements for qudits. By utilizing Heisenberg-Weyl operators, our model suggests that independently of the interaction intensity between the system and the environment, full information about the observable of interest can always be obtained by making the system interact with many environmental qudits, following a quantum Darwinism framework.

We study the effect of local unitary noise on the entanglement evolution of a two-qubit system subject to local monitoring and interqubit coupling by constructing a suitable stochastic path integral based on the Chantasri-Dressel-Jordan formalism. From this, we identify the optimal entanglement dynamics and deploy a diagrammatic method to find a closed-form approximation for the evolution of the average squared concurrence. We find that the optimal trajectory and diagrammatic expansion capture the oscillations of entanglement at short times. A separate numerical analysis of the long-time steady-state entanglement reveals a nonmonotonic relationship between the concurrence and noise strength.

Helium (He) is the ideal atom to perform tests of ab initio calculations in two-electron systems that consider all known effects, including quantum-electrodynamics and nuclear-size contributions. Recent state-of-the-art calculations and measurements of energy intervals involving the He $2{}^3{S}_1$ metastable state reveal discrepancies at the level of $7\sigma$ that require clarification both from the experimental and theoretical sides. We report on a new determination of the ionization energy $E_{\mathrm{I}}\left(2{}^3{S}_1\right)$ of the $\left(1s\right)\left(2s\right){}^3{S}_1$ metastable state of He. The measurements rely on an approach combining interferometric laser-alignment control, SI-traceable frequency calibration, and imaging-assisted Doppler-free spectroscopy. With this approach we record spectra of the $np$ Rydberg series in a highly collimated cold supersonic beam of metastable He generated by a cryogenic valve and an electric discharge. Extrapolation of the Rydberg series yields a new value of the ionization energy [$E_{\mathrm{I}}\left(2{}^3{S}_1\right)/h=1152842742.7082{\left(55\right)}_{\mathrm{stat}}{\left(25\right)}_{\mathrm{sys}}\mathrm{MHz}$] that deviates by $9\sigma$ from the most precise theoretical result [$1152842742.231\left(52\right)\mathrm{MHz}$], reported by Patkóš et al. [Phys. Rev. A 103, 042809 (2021)], confirming earlier discrepancies between experiment and theory in this fundamental system.

Streaked photoelectron emission spectra access the correlated dynamics of photoelectrons and residual target electrons with attosecond temporal resolution. We calculated ab initio single-ionization spectra for photoemission from helium atoms by colinearly polarized ultrashort XUV and assisting few-femtosecond IR pulses. Distinguishing direct and shake-up ionization resulting in ground-state and excited ($n=2,3$) ${\text{He}}^{+}\text{residual}$ ions, respectively, we examined the effects of the correlated photoemission dynamics on the photoelectron phase accumulation as a function of the observable photoelectron detection direction and kinetic energy and XUV–IR pulse delay. We tracked the dynamical evolution of the residual ion in relative streaked photo- emission delays and found dominant contributions for shake-up emission from the residual-ion–photoelectron interaction. These are in very good and fair agreement, respectively, for $n=2$ and $n=3$ shake-up photoemission along the pulse-polarization directions, with previous experimental and theoretical investigations [Ossiander et al., Nat. Phys. 13, 280 (2017)] and reveal a strong photoemission-direction dependence for shake-up ionization due to the coupling between the photoelectron and evolving residual-ion charge distribution in the IR-laser field.

We present an experimental method for the characterization of the kinetic energies of ions confined in a 22-pole radio frequency trap by inducing a small potential barrier using the surrounding ring electrodes, allowing the selective extraction of ions. Energy sampling experiments have been performed on buffer-gas thermalized ${\mathrm{He}}^{+}$ ions at trap temperatures between 10 and 180 K, resulting in distinct extraction curves as a function of the potential barrier, and a differentiated behavior depending on the escape time from the trap. The experiments are complemented by Monte Carlo simulations of the ion trajectories inside the calculated trap potential and allow us to investigate the properties of the sampling method, the role of ion motion coupling, and the impact of residual buffer-gas collisions on the observed results. The technique has also been successfully applied to identify energetic ${{\mathrm{H}}_3}^{+}$ ions produced in an exothermic reaction inside the trap. Upon calibration, this method can provide relative kinetic energy distributions or be used to filter the maximum desired kinetic energy of the ions inside the trap.

We present a technique to assess the spatial aberration content of a focused multiterawatt laser when fired at full power. This method leverages the direct detection of electrons ponderomotively accelerated from the focal volume formed in a low-pressure gaseous backfill. Our results show that the spatial distribution of emitted electrons exhibits distinct features correlated to the laser aberration type and magnitude. This work represents progress toward the complete and accurate in situ spatiotemporal characterization of focused high-intensity lasers.

The most irreducible way to represent information is a sequence of two symbols. In this paper, we construct quantum states using this basic building block. Specifically, we show that the probabilities that arise in quantum theory can be reduced to counting more fundamental ontic states, which we interpret as event networks and model using sequences of 0's and 1's. A completely self-contained formalism is developed for the purpose of organizing and counting these ontic states, which employs the finite cyclic group ${\mathbb{Z}}_2=\{0,1\}$, basic set theory, and combinatorics. This formalism is then used to calculate probability distributions associated with particles of arbitrary spin interacting with sequences of two rotated Stern-Gerlach detectors. These calculations are compared with the predictions of nonrelativistic quantum mechanics and shown to deviate slightly. This deviation can be made arbitrarily small and does not lead to violations of relevant no-go theorems, such as Bell's inequalities, the Kochen-Specker theorem, or the Pusey-Barrett-Rudolph theorem. The proposed model is then extended to an optical system involving photon number states passing through a beam splitter. Leveraging recent advancements in high-precision experiments on these systems, we then propose a means of testing the model using a tabletop experiment.

We investigate the impact of asymmetric perturbations on the perfect transmission resonances (PTRs) of one-dimensional finite periodic systems. With no perturbations, the scattering region consists of $N$ identical cells, and the transmission spectrum exhibits at least $N-1$ PTRs in each passband of the Bloch dispersion of the unit cell. By introducing a perturbation, the periodic structure is broken, which a priori results in the elimination of all PTRs. However, we demonstrate that PTRs can still arise under asymmetric perturbations when the unperturbed system possesses mirror symmetry, utilizing the $\mathcal{PT}$ symmetry of the unperturbed reflectionless eigenvalue problem. We also reveal an intriguing connection between two seemingly independent PTRs that lies in the symmetry of the unperturbed unit cell: If one PTR is preserved, then a dual one is necessarily also preserved. Our findings offer insights for the design of, for example, a robust antireflection setup at multiple wavelengths or all-optical diode devices.

In a recent paper [S.-L. Chen et al., Quantum 5, 552 (2021)], the authors proposed a framework for robustly self-testing steerable quantum assemblages. In this work, we apply their method to the scenario of self-testing two-qubit entangled quantum states. Our bounds on the fidelity with the reference states are compared with other methods.

Quantum computing's promise lies in its intrinsic complexity, with entanglement initially heralded as its hallmark. However, the quest for quantum advantage extends beyond entanglement, encompassing the realm of nonstabilizer (magic) states. Despite their significance, quantifying and characterizing these states pose formidable challenges. Here, we introduce a different approach leveraging convolutional neural networks (CNNs) to classify quantum states based on their nonstabilizerness content. Without relying on a complete knowledge of the state, we utilize partial information acquired from measurement snapshots to train the CNN in distinguishing between stabilizer and nonstabilizer states. Importantly, our methodology circumvents the limitations of full state tomography, offering a practical solution for real-world quantum experiments. In addition, we unveil a theoretical connection between stabilizer Rényi entropies and the expectation value of Pauli matrices for pure quantum states. Our findings pave the way for experimental applications, providing a robust and accessible tool for deciphering the intricate landscape of quantum resources.