In a pure Gaussian tripartition, a range of entanglement between two parties ($AB$) can be purified through classical communication of Gaussian measurements performed within the third ($C$). To begin, this work introduces a direct method to calculate a hierarchic series of projective $C$ measurements for the removal of any $AB$ Gaussian noise, circumventing divergences in prior protocols. Next, a multimode conic framework is developed for pursuing the maximum (Gaussian entanglement of assistance, GEOA) or minimum (Gaussian entanglement of formation, GEOF) pure entanglement that may be revealed or required between $AB$. Within this framework, a geometric necessary and sufficient entanglement condition emerges as a doubly enclosed conic volume, defining a distance metric for conic optimization. Extremizing this distance for spacelike vacuum entanglement in the massless and massive free scalar fields yields (1) the highest known lower bound to GEOA, the first that decays slower than the two-point correlation functions and (2) the lowest known upper bound to GEOF, the first that decays exponentially mirroring the mixed $AB$ negativity. Furthermore, combination of the above with a generalization of previous partially transposed noise filtering techniques allows calculation of a single $C$ measurement that maximizes the purified $AB$ entanglement. Beyond expectation that these behaviors of spacelike GEOA and GEOF persist in interacting theories, the present measurement and optimization techniques are applicable to physical many-body Gaussian states beyond quantum fields.

We demonstrate entanglement between the polarization of an infrared photon and a metastable ${}^{88}\mathrm{Sr}^{+}$ ion qubit. This entanglement persists after transmitting the photon over a $2.8\mathrm{km}$ long commercial fiber deployed in an urban environment. Tomography of the ion-photon entangled state yields a fidelity of 0.949(4) within the laboratory and 0.929(5) after fiber transmission, not corrected for readout errors. Our results establish the strontium ion as a promising candidate for metropolitan-scale quantum networking based on an atomic transition at $1092\mathrm{nm}$, a wavelength compatible with existing telecom fiber infrastructure.

We study the impact of static disorder on a globally controlled superconducting quantum computing architecture based on a quasi-two-dimensional ladder geometry [Phys. Rev. Res. 7, L012065 (2025)]. Specifically, we examine how fabrication-induced inhomogeneities in qubit resonant frequencies and coupling strengths affect quantum state propagation and the fidelity of fundamental quantum operations. Using numerical simulations, we quantify the degradation in performance due to disorder and identify single-qubit rotations, two-qubit entangling gates, and quantum information transport as particularly susceptible. To address this challenge, we rely on pulse optimization schemes and, in particular, on the gradient ascent pulse engineering (GRAPE) algorithm. Our results demonstrate that, even for realistic levels of disorder, optimized pulse sequences can achieve high-fidelity operations, exceeding 99.9% for the three quantum operations, restoring reliable universal quantum logic and robust information flow. These findings highlight pulse optimization as a powerful strategy to enhance the resilience to disorder of solid-state globally driven quantum computing platforms.

We explore a protocol that efficiently charges multiple open quantum batteries in parallel using a single charger. This protocol charges through collective coupling of the charger and the battery to the same thermal reservoir. When applied to multiple quantum batteries, each coupled to different thermal reservoirs, the energy cannot be efficiently transferred from the charger to the battery via collective dissipation alone. We show that the counterintuitive act of incorporating both dissipation and incoherent collective pumping on the charger enables efficient parallel charging of many quantum batteries.

${\mathrm{NaCs}}^{+}$ is theoretically assessed as a candidate platform for coherent optical control of ultracold molecular ions. Through high-level ab initio calculations with scalar-relativistic pseudopotentials, accurate potential energy curves are obtained for the Λ–S states, including Ω-resolved components under spin-orbit coupling. Agreement between the resulting spectroscopic constants and dissociation limits with available data is observed at the few-percent level. From the computed electronic states, $B^2{\mathrm{\Pi }}_{3/2}-X^2{\mathrm{\Sigma }}^{+}$ lifetimes of $25\text{–}31\mathrm{ns}$ are determined and Franck–Condon factors are extensively mapped. Specific $B^2{\mathrm{\Pi }}_{3/2}-X^2{\mathrm{\Sigma }}^{+}$ Raman pathways with favorable overlap products are identified, enabling efficient population transfer into $X^2{\mathrm{\Sigma }}^{+}$ ($v=0$, $J=0$). Combined with a realistic two-color photoassociative-ionization source in a Na–Cs magneto-optical trap overlap, a feasible route to preparing ultracold ${\mathrm{NaCs}}^{+}$ is outlined by our results.

The capability to control molecular rotation for field-free orientation, which arranges molecules in specific spatial directions without external fields, is crucial in physics, chemistry, and quantum information science. However, conventional methods typically lead to transient orientations characterized by periodic directional reversals and necessitate the generation of coherent superpositions across a broad spectrum of rotational states of ultracold molecules. In this work, we develop a theoretical framework for achieving unidirectional field-free orientation by selectively manipulating two specific rotational states of symmetric top molecules. By leveraging the interplay between coherent superpositions and the precise selection of initial states, we demonstrate that both the maximum achievable orientation and its direction can be effectively controlled. To attain the desired two-state orientation, we present a quantum control strategy that utilizes a single control pulse, significantly simplifying the complexities of conventional multistate or multipulse schemes. Numerical simulations validate the effectiveness and feasibility of this approach for methyl iodide (${\mathrm{CH}}_3\mathrm{I}$) molecules, even when accounting for molecular centrifugal distortion. The results highlight the critical roles of initial-state selection and quantum coherence in achieving long-lasting, high unidirectional molecular orientation, opening new directions in stereochemistry, precision spectroscopy, and quantum computing.

We consider the topological properties of the so-called central spin model that consists of $N$ identical spins coupled to a single distinguishable central spin that arises in physical systems such as circuit-QED and bosonic Josephson junctions coupled to an impurity atom. The model closely corresponds to the Su-Schrieffer-Heeger (SSH) model except that the chain of sites in the SSH model is replaced by a chain of states in Fock space specifying the magnetization. We find that the model accommodates topologically protected eigenstates that are "Bell-cat" states consisting of a Schrödinger cat state of the $N$ spins that is maximally entangled with the central spin, and we show how this state can be adiabatically created and moved along the chain by driving the central spin. The Bell-cat states are visualized by plotting their Wigner function, and we explore their robustness against random noise by solving the master equation for the density matrix. We also explain the essential topological difference between identical spins and the excitations of a bosonic mode.

Nonlocal light-matter interactions with giant atoms in high-dimensional environments are not only fundamentally intriguing for testing quantum electrodynamics beyond the dipole approximation but also crucial for building high-dimensional quantum networks and engineering multipartite entangled states. Given the enigmatic and largely uncharted collective signatures exhibited by multiple giant atoms within two-dimensional optical baths, we delve into their nonperturbative collective dynamics within the single-excitation subspace, focusing on the case where they are coupled to a common two-dimensional photonic reservoir and employing a resolvent operator approach. We demonstrate that precisely engineered atomic arrangements lead to unconventional quantum dynamics, featuring non-Markovianity-induced beats and long-lived bound states in the continuum, thereby providing a versatile platform for implementing two-dimensional quantum memory. Phenomenologically, we observe the emergence of exotic photon emission patterns in both two- and three-dimensional (3D) baths. The emission directions are shown to be precisely controllable on demand through exact phase engineering of the coupling parameters, enabling a highly efficient chiral light-matter interface. Moreover, our generalization to a 3D bath reveals that coherent dipole-dipole interactions can survive despite the coupling to a continuum of modes, a finding that challenges conventional wisdom regarding decoherence.

We present a matrix-product-state-based numerical approach for simulating systems composed of several qubits and a common one-dimensional waveguide. In the presented approach, the one-dimensional waveguide is modeled in real space. Thus, one can use the advantage of matrix-product states that are suited for simulating low-entanglement one-dimensional systems. The consequence is that the vacuum of the waveguide in this modeling becomes the Bogoliubov vacuum and one has to consider a not-so-small local Hilbert space for bosonic degrees of freedom. To manage the large local Hilbert space, we adopt the recently proposed single-site schemes. We demonstrate the potential of the presented approach by simulating superradiant phenomena within the Hamiltonian dynamics.

Rydberg atom-based sensors allow for SI traceable measurements and show promise for applications in the field of communication and radar technologies. In this article, we investigate the bandwidth and sensitivity of a Rydberg atom-based sensor in a rubidium vapor cell using Rydberg electromagnetically induced transparency (EIT) spectroscopy. We employ a rf heterodyne measurement technique in combination with an optical homodyne setup to optimize between sensitivity and bandwidth in a Rydberg sensor. While the bandwidth of Rydberg sensor is limited by the Rabi frequency of the coupling field and decoherences, achieving higher bandwidth through smaller beam sizes is thought to compromise sensitivity due to reduced EIT signal strength. Using optical homodyne detection, we demonstrate that sensitivity is preserved while achieving a response bandwidth of $8\mathrm{MHz}$. In addition, by using the Rydberg sensor, we receive digital communication signals and present error vector magnitude measurements as a function of varying symbol rates and the bandwidth of the Rydberg sensor. Furthermore, the sensor's performance is compared with a conventional rf mixer. We establish that the bandwidth of a Rydberg sensor when receiving a pure tone is not the same as the bandwidth of the sensor when receiving a modulated signal. This difference results from the spreading of symbols in the frequency domain, leading to a reduction of the signal-to-noise ratio and an accumulation of noise over the total span of the modulated signal.

The finite speed of light of pulses implies propagation delays between the generation of light, the interaction with different elements along its path, and the final detection at the output of networks and interferometers. We show that it is possible to take these delays into account with a theoretical method which evades quantization of the full continuum of field modes. We illustrate the use of this method by analyzing Ramsey excitation of an atom by a split and delayed quantum pulse.

For any bipartite Gaussian state, Sec. VI in [Phys. Rev. A 72, 022310 (2005)] proposed a quantification of Gaussian entanglement based on Gaussian entanglement witnesses and implemented its numerical calculation through a semidefinite program. However, we demonstrate that this quantification method is flawed and thus cannot be used for the detection of Gaussian entanglement.

In the following, we study the dissipative time evolution of a quantum chain consisting of three coupled harmonic oscillators, the first and third of which weakly interact quadratically with two independent thermal baths in equilibrium at different temperatures. Due to the quadratic form of the total Hamiltonian, the unitary dynamics of the compound system is formally analytically solvable and defines a one-parameter group of Gaussian maps which enables us to solve the exact dynamics of the chain numerically. Following the Gorini-Kossakowski-Sudarshan-Lindblad approach to open quantum systems, one can perform the rotating-wave approximation with respect to the interacting or noninteracting chain Hamiltonian and respectively derive the so-called global and local master equations. The solutions of the ensuing different master equations can then be compared with the exact one, possibly sorting out the two approaches in correspondence to different timescales of the system. We derive the steady states of the open chain quantum dynamics in the two approaches and show that the behavior of fidelity between them versus interoscillator coupling depends on the two bath temperatures, revealing the existence of a temperature-dependent critical interoscillator coupling strength that determines the domain of validity of each approach. When the newly found coupling is less than this critical value, the local approach outperforms the global approach, whereas for larger interoscillator coupling, the global approach is a better approximation of the exact evolution. This critical value of interoscillator coupling depends on the two bath temperatures, which then play a crucial role in deciding the best possible approximating open dynamics.

We develop an extension of the Monte Carlo wave-function approach that unambiguously identifies dynamical entanglement in general composite, open systems. Our algorithm performs tangential projections onto the set of separable states, leading to classically correlated quantum trajectories. By comparing this restricted evolution with the unrestricted one, we can characterize the entangling capabilities of quantum channels without making use of input-output relations. Moreover, applying this method is equivalent to solving the nonlinear master equation in Lindblad form introduced in Pinske et al., Phys. Rev. A 113, L010403 (2026) for two-qubit systems. Our approach also provides a necessary and sufficient condition for entanglement in multipartite systems of arbitrary size, in terms of a stochastic differential equation. Thereby, we isolate the impact of dynamical entanglement in open systems by applying our approach to several correlated decay processes. Therefore, our methodology provides a complete and ready-to-use framework to characterize dynamical quantum correlations caused by arbitrary open-system processes.

Biphoton systems exhibiting entanglement in position-momentum variables, known as spatial entanglement, are among the most intriguing and well-studied phenomena in quantum optics. A notable subset of these is that of phase-entangled states, where entanglement manifests purely through correlations in the spatial phase of the wave function. While the generation of such states from biphotons via spontaneous parametric down-conversion has been explored, their physical implications and applications remain underinvestigated. In this work, we theoretically and experimentally examine a unique form of phase entanglement known as “pure” phase entanglement. This state exhibits the unusual feature that the position of one photon is correlated with the momentum of the other. Unlike typical spatially entangled states, it shows no direct correlation in position or momentum between the two photons, underscoring that all correlations arise purely from the spatial phase of the wave function. We delve deeper into the theory of this state and experimentally construct it from known phase-entangled states. To certify its properties, we propose a setup that performs a “one-particle momentum measurement” and explore the various tunable parameters. We also highlight potential applications of this state in quantum optics and imaging experiments.

Perfect transfer of unknown states across distinct nodes is a basic function in bosonic quantum networks. Here we develop a general theory to construct an $N$-node bosonic network governed by the time-dependent Hamiltonian, as the universal quantum control theory for continuous-variable systems. In particular, we can activate nonadiabatic passages superposed of initial and target modes by the commutation condition about the Hamiltonian's coefficient matrix and projection operator in the representation of time-independent ancillary modes, which serves as the necessary and sufficient condition to solve the time-dependent Schrödinger equation of the full Hamiltonian. To exemplify the versatility of our theory on the Heisenberg-picture passages, we perform arbitrary state exchange between two nodes, chiral entanglement transfer among three bosonic nodes, and chiral Fock-state transfer among three of four bosonic nodes. Our work provides a promising avenue toward the universal control of any pair of nodes or modes as well as the entire bosonic network.

We present a comprehensive framework for constructing various architectures of globally driven quantum computers, with a focus on superconducting qubits. Our approach leverages static inhomogeneities in the Rabi frequencies of qubits controlled by a common classical pulse—a technique we refer to as the “crossed-qubit” method. We detail the essential components and design principles required to realize such systems, highlighting how global control can be harnessed to perform local operations, enabling universal quantum computation. This framework offers a scalable pathway toward quantum processors by striking a balance between wiring complexity and computational efficiency, with potential applications in addressing current challenges to scalability.

We report rovibronic spectra of the $A{}^3\mathrm{\Sigma }^{+}(v^{\prime }=0\text{–}2)$–$X{}^3{\mathrm{\Pi }}_{\mathrm{\Omega }}(v=0)$ rovibronic transitions ($\left|\mathrm{\Omega }\right|=0$,1, and 2) of the ${\mathrm{CO}}^{2+}$ doublycharged molecular ion. Spectra were recorded at high resolution ($\sim 5 {\mathrm{cm}}^{-1}$) in a fast beam of ${\mathrm{CO}}^{2+}$ molecules by detecting the Coulomb explosion of the molecules upon excitation to the $A$ state. Measurements were guided by ab initio calculations, which then assisted the assignment of the observed spectral features. Our results resolve the spin-orbit splittings of the ground vibronic state $X{}^3{\mathrm{\Pi }}_{\mathrm{\Omega }}(v=0)$, but not the rotational structure of the bands due to spectral congestion, and provide spectroscopic information on ${\mathrm{CO}}^{2+}$ with unprecedented resolution. In doing so they expand our knowledge of this benchmark doubly charged molecular ion and expand the short list of doubly charged molecules studied at high resolution.