High-dimensional entanglement offers significant advantages over its low-dimensional counterpart in various information-processing tasks. However, to harness these advantages, it is crucial that the quantum channels used to store or transmit the subsystems of an entangled system not only preserve entanglement but also maintain its dimensionality above a certain threshold. The maximum entanglement dimension that a channel can preserve is referred to as its effective dimensionality since the channel cannot be used to transmit information of dimension greater than that in a single use. In this work, we present a method to certify whether a quantum channel can preserve entanglement dimension above a given threshold. Unlike existing approaches, our method is faithful, i.e., can be applied to any channel, and avoids common assumptions such as preparation of entangled states, auxiliary side channels, and perfect measurement devices. Moreover, the method can be extended to faithfully certify other classes of non-resource-breaking channels, such as non-nonpositive-partial-transpose-breaking (non-NPT-breaking) channels. Finally, we discuss possible experimental realizations of our certification scheme through explicit examples.

Bell or Clauser-Horne-Shimony-Holt (CHSH) tests on superconducting quantum processors are commonly interpreted under the assumption that repeated circuit executions sample a single, stationary-preparation ensemble. Here, we show that this assumption can be violated on contemporary hardware, with direct implications for the interpretation of observed Bell violations. We introduce an ensemble-divergence framework in which the slow temporal drift of the preparation process induces context-dependent effective ensembles, even when measurement independence and locality are preserved. This leads to a relaxed Bell bound $\left|S\right|\le 2+6{\delta }_{\mathrm{ens}}$, where ${\delta }_{\mathrm{ens}}$ quantifies preparation nonstationarity. Because ${\delta }_{\mathrm{ens}}$ is not directly observable, we develop an operational witness ${\delta }_{\mathrm{op}}$ based on bin-resolved outcome statistics for fixed measurement channels. Using Pauli-axis measurements on IBM superconducting processors, we observe statistically significant operational drift that persists after full two-qubit readout mitigation, ruling out measurement artifacts. In contrast, drift extracted from CHSH-optimal measurements is eliminated by mitigation, demonstrating that such settings are unsuitable for diagnosing preparation nonstationarity. We further show that the observed Bell violations imply only modest ensemble divergences, comparable in scale to those required in Hall-type measurement-dependence models, but arising here solely from preparation drift combined with experimental scheduling. While balanced or shuffled scheduling mitigates the operational manifestation of this effect, it does not remove the logical role of the stationary-preparation assumption in the CHSH derivation. Our results identify preparation nonstationarity as a distinct assumption that must be assessed when interpreting Bell-test statistics on noisy intermediate-scale superconducting devices, and highlight the need for drift-aware protocols for reliable quantum certification.

A crucial insight for practical quantum error correction is that different types of errors, such as single-qubit Pauli operators, typically occur with different probabilities. Finding an optimal quantum code under such biased noise is a challenging problem, related to the (generally unknown) maximum capacity of the corresponding noisy channel. A benchmark for this capacity is given by the hashing bound, which describes the performance of random stabilizer codes and leads to the matter of identifying codes that come close to the bound while also being efficiently decodable. In this work, we perform a comprehensive analysis of asymptotically zero-rate holographic codes under biased noise. We show that many representatives from such models of this code class fulfill both the channel optimality and efficient decoding guarantees for tensor-network codes. In fact, all tested holographic codes are found to reach the hashing bound in some bias regime, while several built from the $[[5,1,2]]$ surface code and $[[6,1,3]]$ code exceed state-of-the-art code performance in the 2-Pauli noise regime. Furthermore, we consider Clifford deformations which allow all considered codes to reach the hashing bound for 1-Pauli noise as well. Our results establish that holographic codes, which were previously shown to possess efficient tensor-network decoders, also exhibit competitive thresholds under biased noise.

The maintenance of quantum entanglement lays the elementary building block of quantum information processing, requiring an integration of long coherence time, sufficient storage capacity, and high-fidelity entangling gates. Here, we encode two-qubit entangled states into the decoherence-free subspaces (DFS) of four ions in a cryogenic Paul trap. We apply crosstalk-free sympathetic cooling under dual-type encoding and perform multistate detection that distinguishes the collision-induced leakage error from the qubit levels. By postselecting the leakage-free events, we achieve a storage lifetime of about 1 h for the entangled logical states. We further study the second-order DFS and show its advantage in suppressing the spatially nonuniform noise over the first-order DFS. Our work extends the storage capacity of a DFS quantum memory to support entangled logical states, with wide applications in quantum computing and precision measurement, as well as in each local node of a quantum network.

We propose a measurement-based quantum metrology protocol in a composite model, where the probe system (a spin ensemble) is coupled to an ancillary two-level system (qubit) with a general Heisenberg XXZ interaction. With optimized probe-ancilla coupling strengths and duration of joint evolution, the two parallel evolution paths of the probe system induced by the unconditional measurement on qubit can transform an eigenstate of the collective angular momentum operator of spin ensemble into a two-component state with a large distance in eigenspace. The quantum Fisher information about the phase encoded in the probe system of polarized states or their superposition, that could be relaxed to mixed states, can therefore manifest an exact or asymptotic quadratic scaling with respect to the probe size (spin number) $N$. The quadratic scaling behavior is found to be insensitive to the imperfect encoding operator, polarized direction of probe, and coupling strength. The phase sensitivity can approach the Heisenberg limit by virtue of the parity detection on either ancillary qubit or probe system. This work justifies that the unconditional measurement on a weakly coupled qubit could be an efficient resource to replace Greenberger-Horne-Zeilinger–type states and squeezing Hamiltonian for exceeding the standard quantum limit in metrology precision.

We present and benchmark a type of variational quantum eigensolver (VQE) which we denote $\sigma$-VQE. It is designed to target midspectrum eigenstates and prepare quantum many-body scar states. The approach leverages the fact that noisy intermediate-scale quantum devices are limited in their ability to generate generic highly entangled states. This modified VQE pairs a low-depth circuit with an energy-selective objective that explicitly penalizes energy variance around a chosen target energy. The cost function exploits the limited expressibility of the shallow circuit as atypical low-entanglement eigenstates such as scar states are preferentially selected. We validate this mechanism across two complementary families of models that contain many-body scar states: the Shiraishi-Mori embedding approach and a matrix product state parent Hamiltonian construction. We define an unbiased estimation scheme for the nonlinear cost function that is compatible with qubit-wise commuting grouping and bitstring reuse. A proof-of-principle demonstration using a small-system instance was performed on IBM Fez in December 2025 (Heron r2 QPU). These results motivate its use as a practical algorithm for detecting quantum many-body scars and variationally generating states with appreciable scar state overlap.

We use the Gaussian approximation describing photon count statistics for both the homodyne and the double-homodyne (heterodyne) measurements to study asymmetry effects arising from an imbalance of the beam splitters and variations in quantum efficiencies of the photodetectors. After computing the $Q$ symbols of the positive operator-valued measures (POVMs) of noisy measurements that take into account the asymmetry effects, the operator representations for the POVMs are obtained in the form that assumes applying the additive noise quantum channel to the POVMs of noiseless (ideal) measurements. Additional noise sources are assumed to be represented by statistically independent components included in a single excess-noise parameter that enters the continuous-variable quantum key distribution (CVQKD) analysis. For double-homodyne detection, it was found that the noiseless measurements should generally be expressed in terms of the projectors onto squeezed states and the corresponding squeezed-state operator representation of the POVM along with the measurement noise channel depend on the squeezing parameter that lies in the interval dictated by the condition for the excess noise covariance matrix to be positive semidefinite. The analytical results are used to perform analysis of the asymptotic security of the Gaussian-modulated CVQKD protocol in the untrusted-noise scenario where the measurement noise is assumed to be accessible to an adversary. The inherent non-uniqueness of the operator representation for the double-homodyne POVM manifests itself in the squeezingdependent Holevo information whose extrema determine the lower and upper bounds for the secret fraction. For both types of measurements, the mutual information, the Holevo information, and the asymptotic secret fraction are sensitive to asymmetry effects, leading to degraded performance of the protocol.

In this work, we calculate the hyperfine-structure constants of the ${}^{45}\mathrm{Sc}^{+}$ ion using a relativistic hybrid approach that combines configuration-interaction and coupled-cluster singles and doubles methods. Magnetic-dipole and electric-quadrupole hyperfine-structure constants are determined for the states arising from the $3d4s, 3d^2, 4s^2, 4s4p, 3d4p, 3d5s, 3d4d$, and $3d5p$ configurations. For most of these states, our magnetic-dipole hyperfine-structure constants agree well with available experimental data and represent a substantial improvement over previous theoretical results. By combining our calculated electric-field gradients with the measured electric-quadrupole hyperfine-structure constants for the ${}^{3}F_{2,3,4}, {}^{3}P_{1,2}$, and ${}^{1}G_4$ states within the $3d^2$ configuration, we derive a nuclear quadrupole moment $Q=-0.222\left(5\right)\mathrm{b}$, which is fully consistent with the value recently obtained from molecular data [J.-P. Dognon and P. Pyykkö, Phys. Chem. Chem. Phys. 27, 20453 (2025)].

We present high-precision calculations of isotope shifts for the $2{}^{1}S\text{−}2{}^{3}S$ and $2{}^{3}S\text{−}2{}^{3}P$ transitions in heliumlike ${}^{12,13,14}\mathrm{C}^{4+}$, with mass-shift uncertainties below 5 ppm and field-shift factors determined to $0.1–0.2\%$. Combining theory with experiment yields the mean-square charge-radius difference $\delta {\langle R^2\rangle }^{13,12}=-0.1253\left(66\right){\text{fm}}^2$, consistent with muonic-carbon results at the $1.2\sigma$ level. Using heliumlike ions as a reference, we assess the feasibility of extracting new-physics signatures from isotope shifts. We show that higher-order field-shift nonlinearities can obscure such signals and that the sensitivity to new bosons mediating electron-neutron interactions decreases with nuclear charge. For ${\mathrm{C}}^{4+}$, detecting a new-physics effect comparable to that suggested in helium would require $\delta \langle R^2\rangle$ determinations improved by 2 orders of magnitude. Our work provides a quantitative framework for extracting nuclear charge radii and for assessing potential new-physics signatures beyond the standard model in heliumlike systems.

The discrepancies between theoretical and experimental results in the process of entangled two-photon absorption (ETPA) are not fully understood. Atomic systems are a promising alternative for investigating this process without the systematic effects present in molecules. We present a theoretical study of the ETPA process in cesium atoms, focusing on the $6{}^2{S}_{1/2}\to 8{}^2{S}_{1/2}$ transition. The ETPA cross section is evaluated both with and without the far-off-resonance (FOR) approximation, including the contributions from intermediate atomic states and decoherence effects. The quantum state of light considered is described by the joint-spectral amplitude of photon pairs produced by the spontaneous parametric down-conversion process. When the FOR approximation is applied, the enhancement factor is constant ($36\pi$). In contrast, without this approximation, the enhancement factor oscillates with the entanglement time and achieves a maximum value of approximately 500. These results show the limitations of approximations when calculating the ETPA cross section and contribute to the understanding of the discrepancies between theoretical and experimental values for the ETPA cross section in different samples. The numbers presented in this work can be a starting point for designing experiments aimed at measuring ETPA cross sections in alkali-metal atoms.

We investigate theoretically the coherent dynamics of helium photoionization driven by a pair of time-delayed laser pulses using the $(1+1)$-dimensional two-electron time-dependent Schrödinger equation. Our numerical calculations reveal that the resulting photoelectron spectra exhibit Grobe–Eberly doublets accompanied by Ramsey-like interference fringes. Notably, the contrast of these fringes varies periodically with both laser intensity and interpulse time delay. By evaluating the purity of the reduced density matrix, we attribute this modulation to variations in the bipartite entanglement between the emitted photoelectron and the residual dressed ion. The mechanism controlling the entanglement lies in the interplay between ionic population and coherence, governed by the quantum phase set by the pulse area and the optical phase introduced by the interpulse delay. Moreover, tuning the laser parameters can induce out-of-phase shifts between ion-channel-resolved spectra, providing experimental access to probe entanglement during the buildup of Rabi dynamics via coincidence measurements.

We investigate wetting phenomena between self-bound quantum fluids in a three-component Bose mixture of ${}^{23}\mathrm{Na}, {}^{39}\mathrm{K}$, and ${}^{41}\mathrm{K}$ atoms. Within a density-functional approach including mean-field interactions and Lee-Huang-Yang quantum-fluctuation corrections, we consider two binary quantum liquids formed by components (1, 2) and (2, 3) and study the adsorption of the softer (1, 2) liquid on a stiffer (2, 3) substrate. By tuning the interspecies scattering length $a_{12}$, we show that the surface tension of the (1, 2) liquid can be strongly varied, driving a transition from partial wetting to complete wetting of the (2, 3) phase. The contact angle extracted from cylindrical-cap geometries decreases continuously with increasing $a_{12}$ and vanishes near the critical value $a_{12}^c=-42a_0$. In the complete-wetting regime, a finite amount of (1, 2) liquid wraps around a spherical (2, 3) droplet, producing a self-bound core-shell droplet without external confinement, whose component-1 density has a shell-like, hollow projection. We further show that such shell-shaped quantum droplets can sustain quantized vortical excitations. These results identify wetting as a route to engineering free-standing shell-shaped quantum liquids and suggest possibilities for studying capillarity, topology, and superfluidity in multicomponent quantum droplets.

Boundary time crystals are a class of exotic dissipative quantum phases that spontaneously break continuous time-translation symmetry in the thermodynamic limit of open quantum systems. In finite-size systems, the long-time evolution of boundary time crystals exhibits decaying oscillations that cannot be captured by widely used mean-field theory. To address this issue, we develop an effective approach called the stroboscopic rotating-wave approximation, which provides a well approximated state for the long-time evolution of boundary time crystals in the strongly driven regime. In this approach, the order parameter exhibits both a long-time decaying envelope governed by an effective Lindblad superoperator and short-time oscillations dominated by a reduced quantum dynamical semigroup. Our results reveal that the competition between dephasing processes in three directions induces persistent oscillations, marking the emergence of the boundary-time-crystal phase. We obtain analytical expressions for the steady-state density operator, the oscillation period, and the decay rate of the order parameter when the coherent energy splitting exceeds the dissipation rate. Our work provides a beyond-mean-field tool for studying the dynamics of periodically driven open quantum systems and understanding the formation of time crystals.

Probabilistic error cancellation is an attempt to reverse the effect of dissipative noise channels on quantum computers by applying unphysical channels after the execution of a quantum algorithm on noisy hardware. We investigate on general grounds the properties of such unphysical quantum channels by considering a random-matrix ensemble modeling noisy quantum algorithms. We show that the complex spectra of denoiser channels inherit their structure from random Lindbladians. Additional structure imposed by the locality of noise channels of the quantum computer emerges in terms of a hierarchy of timescales.

A profound comprehension of quantum entanglement is crucial for the progression of quantum technologies. The degree of entanglement can be assessed by enumerating the entangled degrees of freedom, leading to the determination of a parameter known as the Schmidt number (SN). In this paper, we develop an efficient analytical tool for characterizing high-SN witnesses for bipartite quantum states in arbitrary dimensions. Our methods not only offer viable mathematical methods for constructing high-dimensional SN witnesses in theory but also simplify the quantification of entanglement and dimensionality by providing upper bounds for witness coefficients that depend solely on the operator Schmidt coefficient (OSC), thereby reducing computational complexity and enabling straightforward application in arbitrary-dimensional systems without the need for numerical optimization or extensive matrices diagonalization. Most notably, we develop high-dimensional SN witnesses within arbitrary-dimensional systems, with our Schmidt witness coefficients relying solely on the OSC. Subsequently, we demonstrate our theoretical advancements and computational superiority by constructing SN witnesses in arbitrary-dimensional bipartite quantum systems with SNs 4 and 5. In addition, we illustrate the feasibility and superiority of our approach through various numerical examples of mixed states across different dimensions, including low-dimensional cases with SNs 3–6 composed of convex combinations of different orders (both specific and randomly generated examples), as well as high-dimensional cases with SNs 10, 15, and 20, again involving both specific and randomly generated mixed states.

We report a combined experimental and theoretical investigation of the two-body fragmentation dynamics of propylene oxide dication $\left({\mathrm{C}}_3{\mathrm{H}}_6{\mathrm{O}}^{2+}\right)$ induced by highly charged ion $\left({\mathrm{C}}^{5+}\right)$ impact at energy of $112.5\mathrm{keV}/\mathrm{u}$. Using cold-target recoil-ion momentum spectroscopy, we measure the kinetic energy release distributions of four dominant two-body Coulomb explosion channels. To elucidate the underlying dissociation mechanisms, we perform transition state calculations to map the relevant reaction pathways on both singlet and triplet potential energy surfaces. The results reveal that ring opening is the key initial relaxation step for both singlet and triplet states, while the spin multiplicity influences the subsequent isomerization and dissociation processes.

We investigate the microscopic excited-state dynamics initiated by macroscopic propagation of femtosecond laser pulses in low-pressure ${\mathrm{N}}_2$ and ${\mathrm{N}}_2–\mathrm{Ar}$ gas mixtures. Through combined measurements of forward laser transmission and spectrally resolved side-fluorescence emissions of ${\mathrm{N}}_2{}^{+}$ and ${\mathrm{N}}_2$ under various experimental conditions, we reveal a counterintuitive spatial mismatch between the localized on-axis peak intensity and the clamped macroscopic plasma volume. Our results indicate that the sharp decrease of the 391-nm fluorescence signal with increasing pressure is primarily driven by electron-ion collisional quenching, while the reduction in ionization efficiency caused by a slight decrease in peak intensity plays only a minor role. In contrast, the anomalous depletion of the 380-nm fluorescence at relatively higher pressures is caused by the synergistic effect of microscopic collisional quenching, clamping of the effective plasma volume, and plasma density. The experimental observations are well reproduced by solving a comprehensive three-dimensional spatiotemporal nonlinear Schrödinger propagation equation and the proposed fluorescence emission model. This work bridges the gap between macroscopic nonlinear propagation and microkinetic collisional processes, shedding light on the physical picture of the generation and depletion of active species in low-density plasma channels.

We show that a sudden change in the polarization direction of the magnetic dipole moments of the atoms in a dipolar Bose-Einstein condensate (BEC) can serve as a useful dynamical probe to sense its superfluid and solid-like properties. We find that for small angular deviation of the polarization direction, actuated for instance by modifying an external magnetic field, the superfluid state undergoes an undamped scissors-mode oscillation, a characteristic signature of superfluidity. In contrast, both the droplet and supersolid states exhibit a scissors-mode oscillation, which is effectively damped due to multiple closely spaced frequency components. Notably, we find that this damping rate provides a qualitative measure for the rigidity of different phases of a dipolar BEC. Furthermore, there exists a maximum angular deviation of the polarization direction, beyond which the droplet and the supersolid states undergo a permanent deformation, i.e., we find an analog of the usual elastic-to-plastic phase transition of solids. We characterize this transition numerically using the fidelity of the condensate wave function with the ground state, as well as the droplet width and periodicity of the supersolid density of the condensate, which are experimentally accessible. Thus, the dynamical protocol introduced here can be an important experimental benchmark to identify and characterize the superfluid and solid properties of different phases of dipolar BECs.

We study a finite-time thermodynamic refrigeration cycle realized numerically in three-dimensional, weakly interacting Bose-Einstein condensates (BECs). The setup consists of three spatially separated condensates (system, piston, and reservoir) coupled through time-dependent potential barriers that implement compression, expansion, and contact strokes. Finite-temperature initial states are generated with the Stochastic Ginzburg-Landau equation, and the subsequent dynamics are evolved using the truncated Gross-Pitaevskii equation. To measure temperatures we use a momentum-space thermometry method that provides estimates for each condensate. We find that despite mass transfer and sound excitations, the protocol achieves successful cooling during consecutive cycles: the first cycle lowers its temperature by $20\%$ and a second cycle yields additional, though reduced, cooling, reaching a final $27\%$ cooling from the initial state. Our results show that interacting BECs can sustain finite-time quantum thermal cycles under realistic conditions and provide a platform for exploring different refrigeration schemes, optimized control protocols, and shortcuts to adiabaticity.