Non-Markovian effects are often significant when the system-environment coupling is not weak. Indeed, we find that the non-Markovianity is negligible for a single two-level system undergoing pure dephasing via a weak interaction with a harmonic-oscillator environment. In this paper we show that, within the framework of pure dephasing, the non-Markovianity displayed by a two-level system can in fact be far more pronounced. To demonstrate that this is indeed the case, we consider a pure dephasing model where a collection of two-level systems interacts with a common environment. We obtain analytically the dynamics of the collection of the two-level systems and then take a partial trace over all the two-level systems except one. This remaining single two-level system exhibits markedly non-Markovian dynamics, even when the system-environment coupling is weak. This is due to the environment-mediated indirect interaction between the two-level systems. In fact, this indirect interaction can not only increase the non-Markovianity substantially, but also qualitatively change the characteristics of the non-Markovian behavior. For instance, for a single two-level system undergoing pure dephasing, the dynamics is Markovian for both Ohmic and sub-Ohmic environments. This is markedly not the case when we consider multiple two-level systems. These findings provide insights into controlling decoherence in multiqubit quantum systems and have implications for quantum technologies where non-Markovianity can be a resource rather than a limitation.

Steganography is the art of concealing secret information by embedding it in an apparently innocent-looking message. Quantum steganography applies the principles of quantum mechanics to traditional steganography and, compared to the latter, offers significant advantages, including heightened security, improved concealment, and increased data-hiding capacity. Traditionally, quantum steganography disguises the covert communication as channel noise, which is corrected using preshared classical randomness. This method requires the steganalytic eavesdropper Eve to overestimate the level of channel noise, so that the bounds on the stego-channel capacity depend on this assumed gap in Eve's knowledge of the channel. In this work, we point out that by means of preshared quantum entanglement the secret message can be encoded into nonlocal correlations, obviating the need for such an assumption of Eve's ignorance. Consequently, the capacity bounds on the stego channel can then come from the channel capacity of the quantum communication channel. We introduce three such entanglement-based quantum steganographic protocols that make use of catalytic quantum error-correcting codes (QECCs), degenerate entanglement-assisted QECCs, or the phase bit of preshared entanglement. Here catalytic QECCs enable recycling entanglement, while entanglement assistance allows both sender and receiver to contribute to the protocol's secrecy. We derive upper and lower bounds on the secrecy capacity of each protocol, and demonstrate their practical robustness.

We introduce a quantum noise deconvolution technique that requires neither complete knowledge of the noise nor partial noise tomography and is applicable to any invertible quantum noise channel. In this method we construct a set of observables with completely correctable expectation values despite our incomplete knowledge of noise. This task is achieved just by classical postprocessing without extra quantum resources. We show that the number of parameters in the subset of observables with correctable expectation values is the same for all unitary quantum channels. For mixed unitary channels and the assumption that the probability distribution of unitary errors is unknown, we instruct the construction of the set of observables with correctable expectation values. For a particular case where the mixed unitary channel is made of just two random unitary Kraus operators acting on $d$-dimensional Hilbert-space, we show that the observable with a correctable expectation value belongs to a set with at least $d$ parameters. We extend our method by considering observables for which the partial recovery of the expectation value is possible, at the cost of having partial knowledge about the noise-free initial state.

Quantum metrology aims to enhance measurement precision beyond the classical limit by leveraging quantum resources. Unlike multiparameter dynamic quantum metrology, many questions regarding multiparameter quantum metrology at thermal equilibrium remain elusive. In particular, the ultimate precision limits achievable in this equilibrium setting are not yet well understood. In this work, we examine the fundamental limits of estimating multiple parameters with a quantum probe at thermal equilibrium. We first show that the Heisenberg limit with respect to the number of probes can be achieved, and our bound coincides with the known single-parameter bound when only one parameter is estimated. We then consider the low-temperature limit, revealing a qualitatively different behavior compared to the finite-temperature case. We give an example to illustrate the usage of our main results. Finally, we show the conditions under which the sensitivity bound can be attained and the optimal measurements to achieve it.

Solving combinatorial optimization problems using variational quantum algorithms (VQAs) might be a promising application in the NISQ era. However, the limited trainability of VQAs could hinder their scalability to large problem sizes. In this paper we improve the trainability of variational quantum eigensolver (VQE) by utilizing convex interpolation to solve portfolio optimization. Based on convex interpolation, the location of the ground state can be evaluated by learning the property of a small subset of basis states in the Hilbert space. This enlightens naturally the proposals of the strategies of close-to-solution initialization, regular cost function landscape, and recursive ansatz equilibrium partition. The successfully implementation of a 40-qubit demonstration using only 10 superconducting qubits demonstrates the effectiveness of our proposals. Furthermore, the quantum inspiration has also spurred the development of a prototype greedy algorithm. Extensive numerical simulations indicate that the hybridization of VQE and greedy algorithms achieves a mutual complementarity, combining the advantages of both global and local optimization methods. Our proposals can be extended to improve the trainability for solving other large-scale combinatorial optimization problems that are widely used in real applications, paving the way to unleash quantum advantages of NISQ computers in the near future.

Quantum key distribution (QKD) has emerged as a promising solution to protect current cryptographic systems against the threat of quantum computers. As QKD transitions from laboratories to real-world applications, its implementation under various environmental conditions has become a pressing challenge. Major obstacles to practical QKD implementation are the loss of photons in the transmission media and the presence of extreme noise, which can severely limit long-range transmission. In this paper, we investigate the impact of extreme noise on QKD system parameters, including timing jitter, rate-dependent timing shifts, changes in effective detector dead time, and rate-dependent detection efficiency. Contrary to manufacturers' specifications, which assume these parameters to be constant, we demonstrate that these parameters can exhibit significant variations in extreme noise conditions. We show that changes in these parameters play a key role in determining system performance in noisy environments. To address these nonidealities, we develop a model that adapts to detector-dependent timing distortions and recovery effects. In particular, our model is independent of source parameters and can be implemented using data from the detection unit. Our results show that the model enables reliable characterization and optimization of QKD performance under strong noise.

Charge exchange (CX) x-ray spectroscopy is a vital diagnostic tool for astrophysical and fusion plasmas, yet its accuracy is limited by uncertainties in the orbital angular momentum ($l$) distribution of captured electrons. This study presents a systematic evaluation of prevalent $l$-distribution models through laboratory measurements of $L$-shell x-ray emission from ${\mathrm{Ar}}^{16+}$ colliding with He at energies of 1.2–10 keV/u. The measured x-ray spectra and relative line ratios are compared with theoretical results that are calculated with the use of $n$-resolved CX cross sections derived from the multichannel Landau-Zener method combined with various analytical $l$-distribution models and cascade deexcitation branching ratios. A systematic comparison reveals that the statistical $l$-distribution provides the best approximation to the measured spectra across the energy range considered. This work provides reliable atomic data for spectral models that can be used in astrophysical and fusion plasma diagnostics.

To time-resolve attosecond electronic dynamics in general photoionization processes, a technique that retrieves the phase of emitted electronic wave packets without intercepting the interactions is essential. Here, we theoretically demonstrate a scheme that uses isolated attosecond pulses (IAPs) to achieve this goal. Our approach utilizes the coherent interference between the electronic wave packets of interest and the one produced by a subsequent IAP. We show that the photoelectron spectral phase that has eluded direct detection so far can be fully recovered from observable photoelectron spectra without perturbing the electron-release process under investigation. By further performing a time-frequency-like analysis of the photoelectron energy spectra with the spectral phase, we reveal the birth processes of photoelectrons in time and the association between electronic energy and birth time in strong-field ionization driven by circularly polarized laser pulses. The present work explores a promising application of IAPs for ultrafast measurement and opens a viable path for investigating electronic dynamics with quantum phase information.

Clock atom interferometry is an emerging technique in precision measurements that is particularly well suited for sensitivity enhancement through large momentum transfer (LMT). While current systems have demonstrated momentum separations of several hundreds of photon momenta, next-generation quantum sensors are targeting an LMT enhancement factor beyond ${10}^4$. However, the viability of LMT clock interferometers has recently come into question due to the potential impact of laser frequency noise. Here, we resolve this concern by analyzing the cumulative fidelity of sequential state inversions in an LMT atom interferometer. We show that the population error from $n$ pulses applied from alternating directions scales linearly with $n$. This is a significant advantage over the $n^2$ scaling that occurs when probing a two-level system $n$ times from the same direction. We further show that contributions to the interferometer signal from parasitic paths generated by imperfect pulses are negligible, for any loss mechanism. These results establish that laser frequency noise is not a practical limitation for the development of high-fidelity LMT clock atom interferometers.

The transport of intensity equation (TIE) enables deterministic phase retrieval in optical microscopy, yet its application to heterogeneous media exhibiting both refractive-index variations and attenuation remains an open problem. We derive a coupled TIE-TPE (transport of phase equation) framework from the paraxial wave equation with a complex optical potential, in which the refractive index field is decomposed into a spatially uniform mean field and a local fluctuation field through Reynolds decomposition. This formulation yields a nondivergent system of transport equations that simultaneously reconstructs refractive-index fluctuations and attenuation coefficients within the condition $\left|\mathrm{\Delta }n\right|<1$, without requiring linearization or weak-absorption approximations. We establish explicit validity bounds that define the measurable parameter space for a given experimental configuration, emerging from both photon counting statistics and the diffraction limit. Experimental validation using microlens arrays and HeLa cells demonstrates robust recovery of optical properties, including in the transparent-limit regime where attenuation signals approach detection thresholds. We further verify that the attenuation asymmetry parameter remains consistent with zero across three orders of magnitude in optical depth, indicating preservation of optical reciprocity in structurally heterogeneous biological media.

We investigate a theoretical protocol for the dissipative stabilization of mechanical quantum states in a multimode optomechanical system composed of multiple optical and mechanical modes. The scheme employs a single squeezed reservoir that drives one of the optical modes, while the remaining optical modes mediate an effective phonon-phonon interaction Hamiltonian. The interplay between these coherent interactions and the dissipation provided by the squeezed bath enables the steady-state preparation of targeted quantum states of the mechanical modes. In the absence of significant uncontrolled noise sources, the resulting dynamics closely approximate the model introduced in [Zippilli et al., Phys. Rev. Lett. 126, 020402 (2021)]. We analyze the performance of this protocol in generating mechanical cluster states defined on rectangular graphs.

Spectral engineering has enabled the design of electromagnetic structures with enhanced local density of states (LDOS), a key ingredient for wave-mediated technologies. Recent studies motivated by parity-time ($\mathcal{PT}$)-symmetric systems with reactive coupling have suggested that exceptional point (EP) degeneracy may provide a universal route to LDOS enhancement. In this study, we demonstrate that the presence of an EP alone does not guarantee LDOS enhancement. Instead, we rigorously show that EP-induced LDOS enhancement is critically governed by the phase correlation between the coalescing eigenvectors, as revealed by a Green's function formalism combined with Jordan chain analysis. As a result, the maximum LDOS can emerge away from the EP, even in passive systems, in sharp contrast to reactively coupled configurations where the EP coincides with maximal enhancement. Full wave simulations of coupled meta-atoms serve as a representative example that confirms the theoretical predictions and demonstrates experimentally accessible implementations.

In the field of transverse modes, the intrinsic relationship between orbital angular momentum (OAM, $\ell$), which encodes azimuthal twisting, and the radial quantum number $p$, which governs the transverse energy-radius distribution, has long lacked a unified, coordinate-free characterization. In the fixed-order degenerate subspace, it remains an open theoretical question how these degrees of freedom are jointly constrained by a common structure, and how one can distinguish and read out $(p,|\ell \left|\right)$ with minimal information in practice. Starting from symmetry, we prove that while second-order intensity moments are strictly degenerate, fourth-order moments are the first and minimal tier that lifts the $(p,|\ell \left|\right)$ degeneracy. This yields a basis-invariant dimensionless observer $Q$ which turns a structural statement into a single-frame, calibration-free readout. On the engineering side, we exploit the intrinsic order-charge coupling to construct Euler-Hermite-Gaussian (EHG) modes: equal-amplitude, staircase-phase superpositions on the fixed-order ladder whose astigmatic evolution realizes a Dirichlet kernel with strict notches. In a single-parameter “$m$ measurement,” the EHG selector implements a low-crosstalk, near-identity transfer in the $m$ basis; the observer $Q$ then provides a basis-agnostic verification of $(p,|\ell \left|\right)$. This coupling-guided construction yields zero sampling leakage at the designed lattice sites, supports cross-platform, reproducible thresholds under aberrations and apertures, and forms an end-to-end standard operating procedure for state preparation, demultiplexing, and quality control in high-dimensional photonic and quantum links.

We consider stimulated Raman adiabatic passage when the final state is a superposition of two nondegenerate states. The system consists of four states coupled by two light fields. We find the relative phase of the final superposition depends on the relative amplitude, width, and timing of the adiabatic transfer pulses. We discuss these results in the context of experiments measuring symmetry violation in atomic and molecular systems.

Cavity magnomechanics has opened a new frontier in quantum electrodynamics, yielding several significant theoretical and experimental results. In this paper, we propose a different theoretical mechanism to achieve nonreciprocal macroscopic entanglement among magnons, photons, and phonons based on magnon squeezing. Specifically, reversing the squeezing phase, namely, $\theta \to \theta +\pi$, reverses the frequency shift and the effective dissipation rate simultaneously, producing two experimentally distinct configurations that enable nonreciprocal entanglement. Indeed, in contrast to conventional approaches that control only frequency shifts, we show how precise control of the amplitude and phase of the squeezed mode allows us to obtain a tunable nonreciprocity of entanglement. The magnons resulting from the collective motion of the spin in a macroscopic ferrimagnet become coupled to the microwave photons via magnetic dipole interaction and to the phonons via magnetostrictive interaction. Moreover, we show that the proposed scheme achieves ideal nonreciprocity, which can be optimized by cavity-magnon coupling and bath temperature control. Finally, by using the parameters that are experimentally feasible with current technologies, this work provides promising perspectives for hybrid magnon-based quantum technologies.

We propose a phase-difference-estimation algorithm based on tensor-network circuit compression, leveraging time-evolution data to pursue scalability and higher accuracy with a quantum-phase-estimation- (QPE) type algorithm. Using tensor networks, we construct circuits composed solely of nearest-neighbor gates and extract time-evolution data with four-type circuit measurements. In addition, to enhance the accuracy of the time-evolution and state-preparation circuits, we propose techniques based on algorithmic error mitigation and on iterative circuit optimization combined with merging into matrix product states, respectively. Verification using a noiseless simulator for the eight-qubit one-dimensional Hubbard model using an ancilla qubit shows that the proposed algorithm achieves accuracies with 0.4%–4.7% error from a true energy gap with an appropriate time-step size and that accuracy improvements due to the algorithmic error mitigation are observed. We also confirm the enhancement of the overlap with matrix product states through iterative optimization. Finally, the proposed algorithm is demonstrated on IBM Heron devices with Q-CTRL error suppression for 8-, 36-, and 52-qubit models using more than 4000 2-qubit gates. These largest-scale demonstrations for the QPE-type algorithm represent significant progress not only toward practical applications of near-term quantum computing but also toward preparation for the era of error-corrected quantum devices.

We study the entanglement dynamics of $n=2$-, 3-, and 4‐qubit Bell-type and Greenberger-Horne-Zeilinger (GHZ)‐type states under an amplitude‐damping channel (ADC). We quantify multipartite entanglement using the genuine multipartite concurrence (GMC) and evaluate its utility through the optimal teleportation fidelity. For two-qubit states, we analyze the standard (Bennett) teleportation protocol. For three- and four-qubit states, we study controlled quantum teleportation (CQT) with one and two controllers, respectively. Entanglement sudden death (ESD) denotes the abrupt, finite-time disappearance of entanglement caused by decoherence in contrast to asymptotic decay. To counteract ESD, we apply local not (${\widehat{\sigma }}_x$) operations on $m$ of the $n$ qubits ($m\le n$) and derive analytic formulas, revealing that a single-not operation often suffices to alter ESD into asymptotic decay when handling GMC. In contrast, teleportation fidelity can decay more rapidly for single-not flipped states, whereas flipping all qubits is more useful for preserving teleportation fidelity in certain regimes, highlighting that the amount of entanglement alone does not guarantee teleportation utility. Remarkably, in the case of GHZ-type states, ADC-evolved mixed biseparable states can be exploited successfully in the CQT protocol. Further, using the GHZ-symmetric parametrization, we map the two- and three-qubit ADC-evolved mixed states onto a $(x,y)$ plane, revealing their stochastic local operations and classical communication entanglement classes. We also explicitly check the Bell–Clauser-Horne-Shimony-Holt nonlocality hierarchy in the two-qubit teleportation alongside localizable-entanglement diagnostics for three-qubit CQT. Our results clarify the distinct roles of global versus localizable bipartite correlations and suggest simple, experimentally accessible unitary controls for preserving useful quantum resources in noisy channels.

The dual-type qubit scheme is an emerging method to suppress crosstalk errors in scalable trapped-ion quantum computation and quantum networks. Here we report a hardware-economic way to control dual-type ${}^{171}\mathrm{Yb}^{+}$ qubits using a single $355\text{-nm}$ mode-locked pulsed laser. Utilizing its broad frequency comb structure, we drive the Raman transitions of both qubit types encoded in the $S_{1/2}$ and the $F_{7/2}$ hyperfine levels, and probe their carrier transitions and the motional sidebands. We further demonstrate a direct entangling gate between the two qubit types. Our work can simplify the manipulation of the ${}^{171}\mathrm{Yb}^{+}$ qubits both at the hardware and the software level.

Local distinguishability of orthogonal quantum states can be used to reduce the consumption of quantum resources and lower economic costs in quantum protocols. In this paper, we give the local distinguishability of five orthogonal product states (OPSs) on bipartite and tripartite quantum systems. On one hand, we prove that five OPSs, any two of which are orthogonal only on one subsystem, can be perfectly distinguished by local operations and classical communication (LOCC) except one case, and also discuss the local distinguishability of this exceptional case. On the other hand, we conclude that five tripartite OPSs, any two of which are orthogonal only on one subsystem, can be perfectly distinguished by LOCC except two cases. Furthermore, we discuss the local distinguishability of five tripartite OPSs corresponding to these two exceptional cases. Our work provides a detailed characterization of the local distinguishability of five OPSs.

Quantum batteries (QBs) represent a promising platform for the storage and controlled release of energy through the principle of quantum mechanics. By investigating a multilevel QB charged by a sequence of coherent two-level atomic pairs (ancillae), with each atom carrying its own local coherence phase (LCP), we reveal that the coherence phases can be harnessed to optimize the charging dynamics. Specifically, based on the quantum master equation, we show that the charging dynamics of the QB is sensitive to the intra-ancilla LCP difference, while insensitive to their sum. Furthermore, we numerically demonstrate that the ergotropy oscillations can be induced by the coherence of ancilla during charging. Notably, the ergotropy at the first peak always remains at its maximum value, which is in trade-off with the value at saturation. Additionally, we found that the ergotropy oscillations can be effectively suppressed by increasing the LCP difference. And, the antiphase ancillae with maximal LCP difference can diminish the ergotropy oscillations, resulting in a stable charging. In contrast, the in-phase ancillae with minimal LCP difference can lead to the most pronounced ergotropy oscillations, and the first peak remains the highest. These features suggest two distinct operational charging modes: a long-term stable charging mode (charging QB saturation state) using antiphase ancillae and a short-term rapid charging mode (charging QB to the first ergotropy peak) using in-phase ancillae. We have verified that under the optimal short-term rapid charging mode, the overall performance (including ergotropy, charging power, and efficiency) of the coherent QB (CQB) is positively correlated with the battery size (i.e., the number of energy levels of the QB) and is always superior to that of its classical counterpart (i.e., thermal quantum battery, TQB); while under the optimal long-term stable charging mode, although the ergotropy of the CQB also increases monotonically with battery size and exceeds that of the TQB, the charging power and efficiency oscillate with the parity (odd-even) of the battery size, and the odd-sized CQBs outperform the even-sized CQBs. This work highlights coherence phases as a thermodynamic resource for improving the charging performance of QBs and suggests a potential approach to optimizing the design of other quantum devices.