The equivalence between the Schrödinger and Heisenberg representations is a cornerstone of quantum mechanics. However, this relationship remains unclear in the non-Hermitian regime, particularly when the Hamiltonian is time dependent. In this paper, we address this gap by establishing the connection between the two representations, incorporating the metric of the Hilbert space bundle. We not only demonstrate the consistency between the Schrödinger and Heisenberg representations but also present a Heisenberg-like representation grounded in the generalized vielbein formalism, which provides a clear and intuitive geometric interpretation. Unlike the standard Heisenberg representation, where the metric of the Hilbert space is encoded solely in the dual states, the Heisenberg-like representation distributes the metric information between both the states and the dual states. Despite this distinction, it retains the same Heisenberg equation of motion for operators. Within this formalism, the Hamiltonian is replaced by a Hermitian counterpart, while the “non-Hermiticity” is transferred to the operators. Moreover, this approach extends to regimes with a dynamical metric (beyond the pseudo-Hermitian framework) and to systems governed by time-dependent Hamiltonians.

In order to enable the sequential implementation of quantum information-theoretic protocols in the continuous variable framework, we propose two schemes for resource reusability, resource-splitting protocol and unsharp homodyne measurements. We demonstrate the advantage offered by the first scheme in implementing sequential attempts at continuous-variable teleportation when the protocol fails in the previous round. In the second scheme, unsharp quadrature measurements are employed to implement the detection of entanglement between several pairs of observers. Under specific conditions, our calculations show that it is possible to successfully witness the entanglement of the same two-mode state sequentially by as many as five observers.

We introduce a framework for studying multiparty entanglement by analyzing the behavior of collective variables. Throughout the paper, we explore a specific type of multiparty entanglement that can be detected through the fluctuations of a collective observable. We thoroughly analyze its properties and how it can be extended to mixed states while placing it within the context of the existing literature. The novelty of our approach also lies in presenting a graphical point of view. This is done by introducing a spectral space on which the various properties of our entanglement quantifier have a direct pictorial interpretation. Notably, this approach proves particularly effective for assessing $k$ entanglement, as we show its ability to extend previously established inequalities. To enhance understanding, we also demonstrate how this framework applies to specific scenarios, encompassing both finite-dimensional cases and infinite-dimensional systems, the latter being exemplified by the time-frequency modal degree of freedom of copropagating single photons.

We present a general framework for simulating open quantum systems by exploiting the device noise. We find that pseudo-identity unitary transformations on system qubits in the presence of noise can generate nontrivial quantum channels driving open-system dynamics. Controlling parameters in these transformations allows us to simulate selective state-to-state transitions as well as the long-lived coherences found in systems such as photosynthetic light-harvesting complexes. These results suggest a general framework in which parameters in pseudo-identity unitary transformations can be chosen to generate arbitrary nonunitary system-bath channels without any additional qubits representing bath dynamics. The demonstrated controllability of the bath through these transformations establishes different possibilities for the efficient simulation of open quantum systems on quantum devices.

The parabolic convoluted quasi-Sturmian (CQS) approach recently proposed by Zaytsev et al. [Phys. Rev. A 105, 062818 (2022)] to study differential ionization of atomic helium under proton impact is extended to take account of electron capture into the continuum (ECC). In our fully quantum approach, the original four-body proton-helium scattering problem is reduced to finding the continuum state of the Coulomb three-body system $(p^{+},{\text{He}}^{+},e^{-})$; this is accomplished by representing the required wave function in a basis of CQS functions whose asymptotic behavior corresponds to the ionization dynamics. Contrary to the original CQS approach that uses a basis set suitable for describing the two subsystems $(p^{+},{\text{He}}^{+})$ and $(e^{-},{\text{He}}^{+})$, an appropriate set of Jacobi coordinates allows us to construct CQS functions corresponding to the continuous spectrum of the pair $(p^{+},e^{-})$. The extraction of the ionization amplitude from the three-body wave function maintains a closed form character. The extension of the model space by including new basis functions makes it possible to adequately describe the ECC ionization mechanism. Calculations using these CQS functions are presented for 75-keV proton-impact ionization of atomic helium, and for ejected electrons with a velocity far from that of the projectile. Comparison is made with fully differential cross sections (FDCS), measured recently on an absolute scale [Majumdar et al., Phys. Rev. A 110, 032814 (2024)], that show clear signatures of postcollision interactions. The overall agreement between theory and experiment is encouraging. The remaining discrepancies suggest the need to use a combined basis for the correct accounting of the direct ionization channel.

In this study, we investigate the structural properties of the three-body system $\mu {\text{He}}^{+}$ and the four-body system $\mu \text{He}$ using explicitly correlated Gaussian basis functions with global vectors. Our results quantitatively demonstrate the pronounced shielding effect of the muon on the nucleus and reveal structural characteristics of $\mu {\text{He}}^{+}$ and $\mu \text{He}$, analogous to those of H and ${\mathrm{H}}^{-}$, respectively. Using the confined variational method, we examine $s$-wave electron scattering from $\mu {\text{He}}^{+}$ at incident energies below 8.7 eV, considering both ${}^{1}S$ and ${}^{3}S$ symmetries of the two electrons. By fitting near-threshold phase shifts to the modified effective range theory, we determine the scattering lengths to be 5.95 $a_0$ for ${}^{1}S$ symmetry and 1.76 $a_0$ for ${}^{3}S$ symmetry. Finally, we explore the distortion effects on $\mu {\text{He}}^{+}$ induced by electron impact.

Tunneling ionization is one of the basic physical processes in strong-field physics. Photoelectron holographic (PH) interference in tunneling ionization has become one of the research hotspots in strong-field physics. We investigate the interference structure of an Ar atom in orthogonally polarized laser pulses by the quantum-trajectory Monte Carlo (QTMC) model. The results show the “inner spider” holographic interference structure and above-threshold ionization (ATI) ring interference structure in photoelectron momentum distributions (PMDs) of the Ar atom at $\mathrm{\Delta }t=0$. However, as the time delay increases, the interference structure gradually becomes distorted until it is completely destroyed. We find that the interference structure at the PMDs center can only be identified clearly when the time delay has three or fewer optical periods, which indicates that the stability and observability of the interference structure are closely related to the number of periods of the selected time delay. By tracing the trajectories of ionized electrons, we find that the quadrant of the final position of the ionized electron trajectory is consistent with the quadrant of the PMDs for this time window. Furthermore, we find that the inner spider structure disappears when the Coulomb potential is ignored, which is due to the Coulomb focusing effect by analyzing the emission angle of the ionized electrons.

The ionization rate of molecules in strong laser fields depends on the orientation of the ionizing electric field relative to the molecular frame. The orientation dependence of the rate plays an important role in strong-field-based attosecond-scale and imaging methods, motivating us to investigate theoretically whether it can be extracted from the ionization yields or photoelectron momentum distributions obtained by ionization with laser pulses of various polarization forms. As a reference for comparison we use the orientation dependence of the static-field tunneling rate. Numerical solutions of the time-dependent Schrödinger equation for ionization of the ground and first excited states of a model ${\mathrm{HeH}}^{+}$ molecule show that linearly or circularly polarized single-color pulses are of limited use for obtaining the orientation-dependent rate accurately. By adding a second harmonic with suitable polarization, i.e., using either linearly polarized two-color fields or counterrotating circularly polarized two-color fields, the agreement of the extracted signal with the exact tunneling rate is substantially improved.

We propose a theoretical method to realize nonreciprocal light transmission in an optomechanical device assisted by directional quantum squeezing. Specifically, we consider the device consisting of an optomechanical resonator and a nonlinear optical resonator with directional pumping. We find that optical squeezing occurs along the pump direction when the nonlinear resonator is directionally pumped, enabling nonreciprocal light transmission as well as nonreciprocal group delay (slow light) or advancement (fast light). Furthermore, we find that the efficiency of the second-order sidebands can be enhanced in one direction compared with the opposite direction. Our work provides a promising design for the application of directionally squeezed optomechanical devices in nonreciprocal optical communication and signal processing.

We study Hanbury Brown-Twiss spatial intensity correlations in femtosecond laser-fabricated photonic Su-Schrieffer-Heeger lattices using coherent input states with tunable phases. By mapping intensity correlations to the two-body quantum walk, we experimentally simulate edge bound states in the continuum (BICs) of two indistinguishable bosons. These two-body edge BICs show remarkable robustness in the presence of disorder. We then discuss how intensity correlations can capture the dynamics of two identical fermions for which BICs do not exist on the same edge of the lattice. The localization of intensity correlation, observed in the linear regime, persists at weak nonlinearity due to the formation of long-lived edge breathers: spatially localized nonlinear states with oscillating intensity along the propagation distance. For stronger nonlinearities, localized edge states are not formed for a range of phases, destroying the localization of the intensity correlation. Our results highlight the interplay of band structure, initial state, and nonlinearity influencing transport and intensity correlations.

In this paper, we examine the theoretical implications of photonic spin Hall effect (PSHE) amplification in a cavity magnomechanics system. In the framework of the PSHE, we show that spin-orbit interactions cause separation of space across the transverse plane between photons with opposing spins. Our findings reveal that the formation of photonic spin can be tuned across both positive and negative values, depending on the Brewster angle, while varying the magnon-phonon coupling. Notably, we find that in the absence of magnon-phonon coupling, we have magnomechanically induced transparency window at resonance and the PSHE has a higher peak value. Further in the presence of magnon-phonon coupling, the absorption peak occurs at resonance, which leads to a decrease of the PSHE. However, we observe a significant enhancement of the PSHE at two distinct detuning points where light transmission is maximized. Additionally, probe field detuning emerges as a crucial factor in controlling the PSHE. These results suggest that dynamically tuning the coupling between cavity magnons and magnon-phonon modes can greatly enhance the PSHE, presenting new opportunities for advanced nanoscale light manipulation.

Quantum channels represent a broad spectrum of operations crucial to quantum information theory, encompassing everything from the transmission of quantum information to the manipulation of various resources. In the domain of states, the concept of majorization serves as a fundamental tool for comparing the uncertainty inherent in both classical and quantum systems. This paper establishes a rigorous framework for assessing the uncertainty in both classical and quantum channels. By employing a specific class of superchannels, we introduce and elucidate three distinct approaches to channel majorization: constructive, axiomatic, and operational. Intriguingly, these methodologies converge to a consistent ordering. This convergence not only provides a robust basis for defining entropy functions for channels but also clarifies the interpretation of entropy in this broader context. Most notably, our findings reveal that any viable entropy function for quantum channels must assume negative values, thereby challenging traditional notions of entropy.

To push gate performance to levels beyond the thresholds for quantum error correction, it is important to characterize the error sources occurring on quantum gates. However, the characterization of non-Markovian error poses a challenge to current quantum process tomography techniques. Fast Bayesian tomography (FBT) is a self-consistent tomographic protocol that can be bootstrapped from earlier characterization knowledge and be updated in real time with arbitrary gate sequences. Here we demonstrate how FBT allows for the characterization of key non-Markovian error processes. We introduce two experimental protocols for FBT to diagnose the non-Markovian behavior of two-qubit systems on silicon quantum dots. To increase the efficiency and scalability of the experiment-analysis loop, we develop a web-based FBT software stack. To reduce experiment cost and analysis time, we also introduce a native readout method and warm boot strategy. Our results demonstrate that FBT is a useful tool for probing non-Markovian errors that can be detrimental to the ultimate realization of fault-tolerant operation on quantum computing.

We propose a method that uses the “no-jump” evolution of a probe to generate entangled multiparticle states of high fidelity. The probe is coupled to a target ensemble of qubits and engineered to exponentially decay at a rate depending on the target collective spin, such that postselecting on observing no probe decay precisely removes select faster-decaying spin components. When a probe and $N$-qubit target interact via a cavity mode of cooperativity $C$, our procedure generates entangled states with infidelities of $e^{-C/N}$, an exponential improvement over previous carving schemes. This scheme, which we call “counterfactual” carving, can generate complex entangled states for applications in quantum metrology and quantum computing.

In this paper we consider the optimized implementation of multicontrolled Toffoli decomposition using the $\text{Clifford}+T$ gate set. While there are several recent works in this direction, here we explicitly quantify the trade-off (with concrete formulas) between the Toffoli depth (this means the depth using the classical 2-controlled Toffoli gate) of the $n$-controlled Toffoli decomposition and the number of clean ancilla qubits. Additionally, we achieve a reduced Toffoli (consequently $T$) depth, which is an extension of the technique introduced by Khattar and Gidney [T. Khattar and C. Gidney, arXiv:2407.17966]. In terms of a negative result, we first show that by using such conditionally clean ancilla techniques, the Toffoli depth can never achieve exactly $\lceil {log}_{2}n\rceil$, though it remains of the same order. This highlights the limitation of the techniques exploiting conditionally clean ancillas [J. Nie et al., arXiv:2402.05053; T. Khattar and C. Gidney, arXiv:2407.17966]. Then we prove that, in a more general setup, the $T$ depth in the $\text{Clifford}+T$ decomposition, via Toffoli gates, is lower bounded by $\lceil {log}_{2}n\rceil$, and this bound is achieved following the complete binary tree structure. Since the (2-controlled) Toffoli gate can further be decomposed using $\text{Clifford}+T$ gate set, various methodologies are also explored in this regard for trade-off-related implications.

Motivated by experimental realizations of the lattice models with directional tunneling and the generalized bulk-edge correspondence brought by a similarity transformation, we study the topological charge pumping using the Rice-Mele (RM) model with directional tunneling (also termed as the non-Hermitian RM model). In momentum space, through a similaritylike transformation, we map the non-Hermitian RM model to a Hermitian one. Under the biorthogonal basis, the pumping is dictated by a Chern number of the Hermitian RM model. This can be verified by experiments where both the non-Hermitian RM model and its Hermitian conjugation are realized. Under the right-right vector basis, which is relevant to experiments where only the non-Hermitian one is required, we find that the charge pumping contains a dynamical and a topological part. To reveal the topological contribution, an experimental scheme of canceling the dynamical term is proposed.

We present a theory of two-component atomic Fermi superfluid with tunable pairing interaction in a thin spherical shell subject to spin-orbit coupling (SOC). By incorporating SOC into the Fermi superfluid in the BCS-Bose Einstein condensation (BEC) crossover, we obtain the energy spectrum and equations of state. While the order parameter and chemical potential are suppressed by SOC on the BCS side, the former remains positive but the latter may be pushed to negative values by SOC. Meanwhile, the compressibility exhibits kinks as the pairing interaction or SOC varies, indicating singular behavior of higher derivatives of the free energy despite the presence of the superfluid order parameter. The minimum of the energy dispersion indicates a decoupling of the energy gap from the order parameter, and the compressibility kinks occur when the energy gap approaches 0. We found the particle-hole mixing in the Fermi superfluid essential for the compressibility kinks since a Fermi gas with the same SOC but no pairing interaction only exhibits complicated dispersions but no singular behavior. Therefore, our results show that a combination of superfluid, SOC, and geometry can lead to interesting phenomena. We also discuss possible experimental realizations and implications.

Entanglement between light and matter has garnered significant interest for wide-ranging applications in quantum technology. However, weak interactions hinder the generation of entanglement. Here, we propose a scheme to achieve bipartite entanglement through superradiant excitation. The optomechanical entanglement exhibits behavior similar to the critical coupling value of superradiant phase transition. We investigate the effects of critical coupling related parameters, such as effective cavity detuning and cavity dissipation, on entanglement. Notably, strong entanglement can be generated even in the unresolved sideband regime. Increasing the number of atoms can reduce the collective coupling strength required to generate entanglement. Additionally, the entanglement is robust against temperature. Our scheme may provide a degree of freedom to manipulate the entanglement driven by superradiance. Our findings may provide a way to enhance the light-matter interaction via atomic assistance, which may be useful for quantum sensing and quantum information.

We present a quantum theory of diamond masers operating at any temperature using a cavity quantum electrodynamical framework. Special attention is paid to the recently demonstrated room-temperature solid-state masers based on nitrogen-vacancy (NV) defect centers in diamond, but the model can easily be modified for other photoexcited chromophores such as pentacene-doped paraterphenyl, vacancies in silicon-carbide or boron nitride. We show that the eight energy levels involved in the optically pumped NV center polarization process can be mapped to a simple pumped two-level-system. We then derive simple analytical expressions for the optical pump threshold condition for masing as well as the steady-state microwave output power which can be used to design and predict maser performance. Finally, we investigate second-order correlations and find that typical diamond masers operate in an intermediate regime between the good and bad cavity limits where photon emission is driven by both stimulated and superradiant processes.

In this article, we present a stochastic collective density-matrix approach to numerically study the conditional dynamics of large systems of identical particles in the presence of individual and collective dissipation, as described by stochastic master equations. To illustrate the application potential of the approach, we use it to study the conditional spin squeezing of hundreds of identical atoms in a bad optical cavity subject to homodyne detection. We demonstrate that the conditional spin squeezing can be vividly illustrated by a Gaussian-like distribution on the quantum states of the atomic ensemble, and we examine the influence of various processes, such as the individual atomic dissipation, on this distribution. In the future, the present approach can be used to reveal measurement effects of multiple-level atoms system, to explore generation of exotic nonclassical states, such as cat states, and to gauge approximate approaches, such as the stochastic mean-field approach.